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Volumn 46, Issue 1, 2009, Pages 1-33

Why are solitons stable?

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EID: 58649105782     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-08-01228-7     Document Type: Article
Times cited : (140)

References (87)
  • 1
    • 0016369301 scopus 로고
    • The inverse scattering transform-Fourier analysis for nonlinear problems
    • MR0450815 (56:9108).
    • M. Ablowitz, D. Kaup, A. Newell, H. Segur, The inverse scattering transform-Fourier analysis for nonlinear problems. Studies in Appl. Math. 53 (1974), 249-315. no. 4, MR0450815 (56:9108)
    • (1974) Studies in Appl. Math. , vol.53 , Issue.4 , pp. 249-315
    • Ablowitz, M.1    Kaup, D.2    Newell, A.3    Segur, H.4
  • 2
    • 0000363750 scopus 로고
    • The stability of solitary waves
    • MR0338584 (49:3348).
    • T.B. Benjamin, The stability of solitary waves, Proc. Roy. Soc. London Ser. A 328 (1972), 153-183. MR0338584 (49:3348)
    • (1972) Proc. Roy. Soc. London Ser. A , vol.328 , pp. 153-183
    • Benjamin, T.B.1
  • 3
    • 0042516360 scopus 로고
    • Existence of a ground state in nonlinear equations of the Klein-Gordon type
    • (Proc. Internat. School, Erice, 1978), Wiley, Chichester, MR578738 (81i:35137).
    • H. Berestycki, P.-L. Lions, Existence of a ground state in nonlinear equations of the Klein-Gordon type, Variational inequalities and complementarity problems (Proc. Internat. School, Erice, 1978), pp. 35-51, Wiley, Chichester, 1980. MR578738 (81i:35137)
    • (1980) Variational inequalities and complementarity problems , pp. 35-51
    • Berestycki, H.1    Lions, P-L.2
  • 5
    • 0000133747 scopus 로고
    • On the stability theory of solitary waves
    • MR0386438 (52:7292).
    • J. Bona, On the stability theory of solitary waves, Proc. Roy. Soc. London Ser. A 344 (1975), no. 1638, 363-374. MR0386438 (52:7292)
    • (1975) Proc. Roy. Soc. London Ser. A , vol.344 , Issue.1638 , pp. 363-374
    • Bona, J.1
  • 7
    • 0023648120 scopus 로고
    • Stability and instability of solitary waves of Korteweg-de Vries type
    • MR897729 (88m:35128).
    • J. Bona, P.E. Souganidis, W. Strauss, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. Roy. Soc. London Ser. A. 411 (1987), 395-412. MR897729 (88m:35128)
    • (1987) Proc. Roy. Soc. London Ser. A , vol.411 , pp. 395-412
    • Bona, J.1    Souganidis, P.E.2    Strauss, W.3
  • 8
    • 0002779183 scopus 로고
    • On the stability of solitary waves for nonlinear Schr̈odinger equations
    • Amer. Math. Soc. Transl. Ser. 2 164, Amer. Math. Soc. Providence, RI, 1995 MR1334139 (96e:35157).
    • V.S. Buslaev, G.S. Perelman, On the stability of solitary waves for nonlinear Schr̈odinger equations, Nonlinear evolution equations 75-98, Amer. Math. Soc. Transl. Ser. 2 164, Amer. Math. Soc. Providence, RI, 1995 MR1334139 (96e:35157)
    • (1995) Nonlinear evolution equations , pp. 75-98
    • Buslaev, V.S.1    Perelman, G.S.2
  • 9
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger equations
    • New York University, Courant Institute of Mathematical Sciences, AMS, MR2002047 (2004j:35266).
    • T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, AMS, 2003. MR2002047 (2004j:35266)
    • (2003) Courant Lecture Notes in Mathematics , vol.10
    • Cazenave, T.1
  • 10
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • MR677997 (84i:81015).
    • T. Cazenave, P.L. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys. 85 (1982), 549-561. MR677997 (84i:81015)
    • (1982) Comm. Math. Phys. , vol.85 , pp. 549-561
    • Cazenave, T.1    Lions, P.L.2
  • 11
    • 0015249887 scopus 로고
    • 3 = 0 and a variational characterization of other solutions
    • MR0333489 (48:11814).
    • 3 = 0 and a variational characterization of other solutions, Arch. Rat. Mech. Anal. 46 (1972), 81-95. MR0333489 (48:11814)
    • (1972) Arch. Rat. Mech. Anal. , vol.46 , pp. 81-95
    • Coffman, C.V.1
  • 12
    • 33749339365 scopus 로고    scopus 로고
    • Large data wave operator for the generalized Korteweg-de Vries equations
    • MR2194502 (2006i:35309).
    • R. Côte, Large data wave operator for the generalized Korteweg-de Vries equations, Differential and Integral Equations, 19 (2006), no. 2, 163-188. MR2194502 (2006i:35309)
    • (2006) Differential and Integral Equations , vol.19 , Issue.2 , pp. 163-188
    • Côte, R.1
  • 15
    • 57049099179 scopus 로고    scopus 로고
    • A survey on asymptotic stability of ground states of nonlinear Schrödinger equations
    • Quad. Mat., 15, Dept. Math., Seconda Univ. Napoli, Caserta, MR2231327 (2007h:35311).
    • S. Cuccagna, A survey on asymptotic stability of ground states of nonlinear Schrödinger equations, Dispersive nonlinear problems in mathematical physics, 21-57, Quad. Mat., 15, Dept. Math., Seconda Univ. Napoli, Caserta, 2004. MR2231327 (2007h:35311)
    • (2004) Dispersive nonlinear problems in mathematical physics , pp. 21-57
    • Cuccagna, S.1
  • 16
    • 84980148411 scopus 로고
    • Inverse scattering on the line
    • MR512420 (80e:34011).
    • P. Deift; E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979), no. 2, 121-251. MR512420 (80e:34011)
    • (1979) Comm. Pure Appl. Math. , vol.32 , Issue.2 , pp. 121-251
    • Deift, P.E.1    Trubowitz, E.2
  • 17
    • 0346343593 scopus 로고    scopus 로고
    • Stabilité asymptotique des ondes solitaires de l'équation de Benjamin-Bona-Mahony
    • MR2030105 (2004j:35242).
    • K. El Dika, Stabilité asymptotique des ondes solitaires de l'équation de Benjamin-Bona-Mahony, C. R. Acad. Sci. Paris, Ser. I, 337 (2003), 649-652. MR2030105 (2004j:35242)
    • (2003) C. R. Acad. Sci. Paris, Ser. I , vol.337 , pp. 649-652
    • El Dika, K.1
  • 19
    • 0003530086 scopus 로고
    • Studies of nonlinear problems I
    • A.C. Newell ed., American Mathematical Society, Providence, R.I. MR0336014 (49:790).
    • E. Fermi, J. Pasta, S. Ulam, Studies of nonlinear problems I, Los Alamos Report LA1940 (1955); reproduced in Nonlinear Wave Motion, A.C. Newell ed., American Mathematical Society, Providence, R.I. 1974, pp. 143-156. MR0336014 (49:790)
    • (1974) Los Alamos Report LA1940 (1955); reproduced in Nonlinear Wave Motion , pp. 143-156
    • Fermi, E.1    Pasta, J.2    Ulam, S.3
  • 22
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrodinger operators
    • MR0460850 (57:842).
    • R.T. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrodinger operators, J. Math. Phys. 8 (1977), 1794-1797. MR0460850 (57:842)
    • (1977) J. Math. Phys. , vol.8 , pp. 1794-1797
    • Glassey, R.T.1
  • 23
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry
    • MR901236 (88g:35169).
    • M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry. I., J. Funct. Anal. 74 (1987), 160-197. MR901236 (88g:35169)
    • (1987) I. J. Funct. Anal. , vol.74 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 24
    • 35949040541 scopus 로고
    • Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons
    • R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192-1194
    • (1971) Phys. Rev. Lett. , vol.27 , pp. 1192-1194
    • Hirota, R.1
  • 25
    • 0003760449 scopus 로고    scopus 로고
    • Integrable systems. Twistors, loop groups, and Riemann surfaces
    • Oxford, September 1997. Oxford Graduate Texts in Mathematics, 4. The Clarendon Press, Oxford University Press, New York, MR1723384 (2000g:37003).
    • N.J. Hitchin, G.B. Segal, R.S. Ward, Integrable systems. Twistors, loop groups, and Riemann surfaces. Lectures from the Instructional Conference held at the University of Oxford, Oxford, September 1997. Oxford Graduate Texts in Mathematics, 4. The Clarendon Press, Oxford University Press, New York, 1999. MR1723384 (2000g:37003)
    • (1999) Lectures from the Instructional Conference held at the University of Oxford
    • Hitchin, N.J.1    Segal, G.B.2    Ward, R.S.3
  • 26
    • 34547337563 scopus 로고    scopus 로고
    • Fast soliton scattering by delta impurities
    • MR2318852 27.
    • J. Holmer, J. Marzuola, M. Zworski, Fast soliton scattering by delta impurities, Comm. Math. Phys. 274 (2007), 187-216. MR2318852 27
    • (2007) Comm. Math. Phys. , vol.274 , pp. 187-216
    • Holmer, J.1    Marzuola, J.2    Zworski, M.3
  • 28
    • 33750526878 scopus 로고    scopus 로고
    • Global well-posedness, scattering, and blowup for the energy-critical, focusing, non-linear Schrödinger equation in the radial case
    • MR2257393 (2007g:35232).
    • C. Kenig and F. Merle, Global well-posedness, scattering, and blowup for the energy-critical, focusing, non-linear Schrödinger equation in the radial case, Invent. Math. 166 (2006), 645-675. MR2257393 (2007g:35232)
    • (2006) Invent. Math. , vol.166 , pp. 645-675
    • Kenig, C.1    Merle, F.2
  • 29
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • MR1211741 (94h:35229).
    • C. Kenig, G. Ponce, L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Commun. Pure Appl. Math. 46 (1993), 527-560. MR1211741 (94h:35229)
    • (1993) Commun. Pure Appl. Math. , vol.46 , pp. 527-560
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 32
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • D.J. Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. 539 (1895), 422-443.
    • (1895) Philos. Mag. , vol.539 , pp. 422-443
    • Korteweg, D.J.1    de Vries, G.2
  • 33
    • 33749459423 scopus 로고    scopus 로고
    • Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension
    • MR2219305 (2007b:35301).
    • J. Krieger, W. Schlag, Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension, J. Amer. Math. Soc. 19 (2006), 815-920. MR2219305 (2007b:35301)
    • (2006) J. Amer. Math. Soc. , vol.19 , pp. 815-920
    • Krieger, J.1    Schlag, W.2
  • 36
    • 38349190717 scopus 로고    scopus 로고
    • Renormalization and blow up for charge one equivariant critical wave maps
    • MR2372807.
    • J. Krieger, W. Schlag, D. Tataru, Renormalization and blow up for charge one equivariant critical wave maps, Invent. Math. 171 (2008), 543-615. MR2372807
    • (2008) Invent. Math. , vol.171 , pp. 543-615
    • Krieger, J.1    Schlag, W.2    Tataru, D.3
  • 38
    • 0011111544 scopus 로고    scopus 로고
    • Analysis of Hamiltonian PDEs
    • 19. Oxford University Press, Oxford, MR1857574 (2002k:35054).
    • S. Kuksin, Analysis of Hamiltonian PDEs. Oxford Lecture Series in Mathematics and its Applications, 19. Oxford University Press, Oxford, 2000. MR1857574 (2002k:35054)
    • (2000) Oxford Lecture Series in Mathematics and its Applications
    • Kuksin, S.1
  • 39
  • 40
    • 1642328742 scopus 로고    scopus 로고
    • 2-compact solutions of the generalized Korteweg-de Vries equations
    • MR2038148 (2005e:35202).
    • 2-compact solutions of the generalized Korteweg-de Vries equations, Comm. Partial Diff. Eq. 29 (2004), 157-171. MR2038148 (2005e:35202)
    • (2004) Comm. Partial Diff. Eq. , vol.29 , pp. 157-171
    • Laurent, C.1    Martel, Y.2
  • 41
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • MR0235310 (38:3620).
    • P.D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968), 467-490. MR0235310 (38:3620)
    • (1968) Comm. Pure Appl. Math. , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 42
    • 27544509563 scopus 로고    scopus 로고
    • Asymptotic N-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations
    • MR2170139 (2007a:35128).
    • Y. Martel, Asymptotic N-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations, Amer. J. Math. 127 (2005), 1103-1140. MR2170139 (2007a:35128)
    • (2005) Amer. J. Math. , vol.127 , pp. 1103-1140
    • Martel, Y.1
  • 43
    • 34249016378 scopus 로고    scopus 로고
    • Linear problems related to asymptotic stability of solitons of the generalized KdV equations
    • MR2262941 (2007i:35204).
    • Y. Martel, Linear problems related to asymptotic stability of solitons of the generalized KdV equations, SIAM J. Math. Anal. 38 (2006), 759-781. MR2262941 (2007i:35204)
    • (2006) SIAM J. Math. Anal. , vol.38 , pp. 759-781
    • Martel, Y.1
  • 44
    • 0034164847 scopus 로고    scopus 로고
    • A Liouville theorem for the critical generalized Korteweg-de Vries equation
    • MR1753061 (2001i:37102).
    • Y. Martel, F. Merle, A Liouville theorem for the critical generalized Korteweg-de Vries equation, J. Math. Pures Appl. 79 (2000), 339-425. MR1753061 (2001i:37102)
    • (2000) J. Math. Pures Appl. , vol.79 , pp. 339-425
    • Martel, Y.1    Merle, F.2
  • 45
    • 0035609368 scopus 로고    scopus 로고
    • Asymptotic stability of solitons for subcritical generalized KdV equations
    • MR1826966 (2002b:35182).
    • Y. Martel, F. Merle, Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Rat. Mech. Anal. 157 (2001), no. 3, 219-254. MR1826966 (2002b:35182)
    • (2001) Arch. Rat. Mech. Anal. , vol.157 , Issue.3 , pp. 219-254
    • Martel, Y.1    Merle, F.2
  • 46
    • 0036016142 scopus 로고    scopus 로고
    • 2-critical generalized KdV equation
    • MR1896235 (2003c:35142).
    • 2-critical generalized KdV equation, J. Amer. Math. Soc. 15 (2002), no. 3, 617-664. MR1896235 (2003c:35142)
    • (2002) J. Amer. Math. Soc. , vol.15 , Issue.3 , pp. 617-664
    • Martel, Y.1    Merle, F.2
  • 47
    • 0036872989 scopus 로고    scopus 로고
    • 2-mass for the critical gKdV equation
    • MR1944576 (2003j:35281).
    • 2-mass for the critical gKdV equation Duke Math. J. 115 (2002), no. 2, 385-408. MR1944576 (2003j:35281)
    • (2002) Duke Math J. , vol.115 , Issue.2 , pp. 385-408
    • Martel, Y.1    Merle, F.2
  • 48
    • 0036000529 scopus 로고    scopus 로고
    • Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
    • MR1888800 (2003e:35270).
    • Y. Martel, F. Merle, Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation, Ann. Math. 155 (2002), 235-280. MR1888800 (2003e:35270)
    • (2002) Ann. Math. , vol.155 , pp. 235-280
    • Martel, Y.1    Merle, F.2
  • 49
    • 11844251264 scopus 로고    scopus 로고
    • Asymptotic stability of solitons of the subcritical gKdV equations revisited
    • MR2109467 (2006i:35319).
    • Y. Martel, F. Merle, Asymptotic stability of solitons of the subcritical gKdV equations revisited, Nonlinearity 18 (2005), no. 1, 55-80. MR2109467 (2006i:35319)
    • (2005) Nonlinearity , vol.18 , Issue.1 , pp. 55-80
    • Martel, Y.1    Merle, F.2
  • 50
    • 41649103047 scopus 로고    scopus 로고
    • Refined asymptotics around solitons for gKdV equations
    • MR2358258.
    • Y. Martel, F. Merle, Refined asymptotics around solitons for gKdV equations, Discrete Contin. Dyn. Syst. 20 (2008), no. 2, 177-218. MR2358258
    • (2008) Discrete Contin. Dyn. Syst. , vol.20 , Issue.2 , pp. 177-218
    • Martel, Y.1    Merle, F.2
  • 55
    • 58649095566 scopus 로고    scopus 로고
    • Qualitative results on the generalized critical KdV equation
    • New Stud. Adv. Math., 2, Int. Press, Somerville, MA, MR2055847 (2005f:35272).
    • Y. Martel, F. Merle, Qualitative results on the generalized critical KdV equation, Lectures on partial differential equations, 175-179, New Stud. Adv. Math., 2, Int. Press, Somerville, MA, 2003. MR2055847 (2005f:35272)
    • (2003) Lectures on partial differential equations , pp. 175-179
    • Martel, Y.1    Merle, F.2
  • 56
    • 0036882736 scopus 로고    scopus 로고
    • Stability and asymptotic stability in the energy space for the sum of N solitons for the subcritical gKdV equations
    • MR1946336 (2003j:35280).
    • Y. Martel, F. Merle, T.-P. Tsai, Stability and asymptotic stability in the energy space for the sum of N solitons for the subcritical gKdV equations, Commun. Math. Phys. 231 (2002), 347-373. MR1946336 (2003j:35280)
    • (2002) Commun. Math. Phys. , vol.231 , pp. 347-373
    • Martel, Y.1    Merle, F.2    Tsai, T.-P.3
  • 57
    • 33746039746 scopus 로고    scopus 로고
    • 1 for the sum of K solitary waves to some nonlinear Schrödinger equations
    • MR2228459 (2007f:35271).
    • 1 for the sum of K solitary waves to some nonlinear Schrödinger equations, Duke Math. J. 133 (2006), 405-466. MR2228459 (2007f:35271)
    • (2006) Duke Math. J. , vol.133 , pp. 405-466
    • Martel, Y.1    Merle, F.2    Tsai, T.-P.3
  • 58
    • 84974001368 scopus 로고
    • Determination of blow-up solutions with minimal mass for nonlinear Schrodinger equation with critical power
    • MR1203233 (94b:35262).
    • F. Merle, Determination of blow-up solutions with minimal mass for nonlinear Schrodinger equation with critical power, Duke Math. J. 69 (1993), 427-453. MR1203233 (94b:35262)
    • (1993) Duke Math. J. , vol.69 , pp. 427-453
    • Merle, F.1
  • 59
    • 0035616659 scopus 로고    scopus 로고
    • Existence of blow-up solutions in the energy space for the critical generalized KdV equation
    • MR1824989 (2002f:35193).
    • F. Merle, Existence of blow-up solutions in the energy space for the critical generalized KdV equation, J. Amer. Math. Soc. 14 (2001), 555-578. MR1824989 (2002f:35193)
    • (2001) J. Amer. Math. Soc. , vol.14 , pp. 555-578
    • Merle, F.1
  • 60
    • 0041350485 scopus 로고    scopus 로고
    • Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
    • MR1995801 (2005j:35207).
    • F. Merle, P. Raphael, Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation, Geom. Funct. Anal. 13 (2003), no. 3, 591-642. MR1995801 (2005j:35207)
    • (2003) Geom. Funct. Anal. , vol.13 , Issue.3 , pp. 591-642
    • Merle, F.1    Raphael, P.2
  • 61
    • 2942586742 scopus 로고    scopus 로고
    • 2 critical nonlinear Schrödinger equation
    • MR2061329 (2006a:35283).
    • 2 critical nonlinear Schrödinger equation, Invent. Math. 156 (2004), no. 3, 565-672. MR2061329 (2006a:35283)
    • (2004) Invent. Math. , vol.156 , Issue.3 , pp. 565-672
    • Merle, F.1    Raphael, P.2
  • 62
    • 20444437961 scopus 로고    scopus 로고
    • The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
    • MR2150386 (2006k:35277).
    • F. Merle, P. Raphael, The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation, Ann. of Math. (2) 161 (2005), no. 1, 157-222. MR2150386 (2006k:35277)
    • (2005) Ann. of Math. (2) , vol.161 , Issue.1 , pp. 157-222
    • Merle, F.1    Raphael, P.2
  • 63
    • 0034407299 scopus 로고    scopus 로고
    • A Liouville theorem for vector-valued nonlinear heat equations and applications
    • MR1735081 (2001d:35084).
    • F. Merle, H. Zaag, A Liouville theorem for vector-valued nonlinear heat equations and applications, Math. Ann. 316 (2000), no. 1, 103-137. MR1735081 (2001d:35084)
    • (2000) Math. Ann. , vol.316 , Issue.1 , pp. 103-137
    • Merle, F.1    Zaag, H.2
  • 64
    • 36849110505 scopus 로고
    • Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation
    • MR0252825 (40:6042a).
    • R. Miura, Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation, J. Math. Phys. 9 (1968), 1202-1204. MR0252825 (40:6042a)
    • (1968) J. Math. Phys. , vol.9 , pp. 1202-1204
    • Miura, R.1
  • 65
    • 0016973738 scopus 로고
    • The Korteweg-de Vries equation: a survey of results
    • MR0404890 (53:8689).
    • R. Miura, The Korteweg-de Vries equation: a survey of results, SIAM Review 18 (1976), 412-459. MR0404890 (53:8689)
    • (1976) SIAM Review , vol.18 , pp. 412-459
    • Miura, R.1
  • 66
    • 2442646154 scopus 로고    scopus 로고
    • Asymptotic stability of solitary wave solutions to the regularized long-wave equation
    • MR2052617 (2005h:35299).
    • T. Mizumachi, Asymptotic stability of solitary wave solutions to the regularized long-wave equation, J. Differential Equations 200 (2004), no. 2, 312-341. MR2052617 (2005h:35299)
    • (2004) J. Differential Equations , vol.200 , Issue.2 , pp. 312-341
    • Mizumachi, T.1
  • 67
    • 0039847915 scopus 로고
    • Asymptotic behaviour as t→∞ of the solution to the Cauchy problem for a nonlinear Schrödinger equation (Russian)
    • MR568535 (81f:81015).
    • V. J. Novoksenov, Asymptotic behaviour as t→∞ of the solution to the Cauchy problem for a nonlinear Schrödinger equation (Russian), Dokl. Akad. Nauk SSSR 251 (1980), 799-802. MR568535 (81f:81015)
    • (1980) Dokl. Akad. Nauk SSSR , vol.251 , pp. 799-802
    • Novoksenov, V.J.1
  • 68
    • 21844510556 scopus 로고
    • Asymptotic stability of solitary waves
    • MR1289328 (95h:35209).
    • R. Pego, M.Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys. 164 (1994), no. 2, 305-349. MR1289328 (95h:35209)
    • (1994) Comm. Math. Phys. , vol.164 , Issue.2 , pp. 305-349
    • Pego, R.1    Weinstein, M.2
  • 69
    • 8744309907 scopus 로고    scopus 로고
    • Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations
    • MR2097576 (2005g:35277).
    • G.S. Perelman, Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations, Comm. Partial Diff. Eq. 29 (2004), 1051-1095. MR2097576 (2005g:35277)
    • (2004) Comm. Partial Diff. Eq. , vol.29 , pp. 1051-1095
    • Perelman, G.S.1
  • 70
    • 11844298384 scopus 로고    scopus 로고
    • Asymptotic stability of N-soliton states of NLS
    • MR2094850 (2005i:81181).
    • I. Rodnianski, W. Schlag, A. D. Soffer, Asymptotic stability of N-soliton states of NLS, Comm. Pure Appl. Math. 58 (2005), no. 2, 149-216. MR2094850 (2005i:81181)
    • (2005) Comm. Pure Appl. Math. , vol.58 , Issue.2 , pp. 149-216
    • Rodnianski, I.1    Schlag, W.2    Soffer, A.D.3
  • 73
    • 36749115189 scopus 로고
    • Asymptotic solutions and conservation laws for the nonlinear Schrödinger equation I
    • MR0450822 (56:9115a).
    • H. Segur, M. Ablowitz, Asymptotic solutions and conservation laws for the nonlinear Schrödinger equation I. J. Math. Phys. 17 (1976), 710-713. MR0450822 (56:9115a)
    • (1976) J. Math. Phys. , vol.17 , pp. 710-713
    • Segur, H.1    Ablowitz, M.2
  • 74
    • 35949020007 scopus 로고
    • Kinetic equations from Hamiltonian dynamics: Markovian limits
    • MR578142 (81e:82010).
    • H. Spohn, Kinetic equations from Hamiltonian dynamics: Markovian limits, Rev. Mod. Phys. 52 (1980), 569-615. MR578142 (81e:82010)
    • (1980) Rev. Mod. Phys. , vol.52 , pp. 569-615
    • Spohn, H.1
  • 75
    • 0004136765 scopus 로고
    • Princeton University Press, MR1232192 (95c:42002).
    • E. M. Stein, Harmonic Analysis, Princeton University Press, 1993. MR1232192 (95c:42002)
    • (1993) Harmonic Analysis
    • Stein, E.M.1
  • 76
    • 47749149259 scopus 로고    scopus 로고
    • Soliton dynamics and scattering
    • Madrid MR2275691 (2008a:35268).
    • A. Soffer, Soliton dynamics and scattering, Proc. Internat. Congress of Math., Madrid 2006, Vol. III, 459-472. MR2275691 (2008a:35268)
    • (2006) Proc. Internat. Congress of Math. , vol.3 , pp. 459-472
    • Soffer, A.1
  • 77
    • 15944416090 scopus 로고    scopus 로고
    • On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation
    • MR2091393 (2005j:35210).
    • T. Tao, On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation, Dynamics of PDE 1 (2004), 1-48. MR2091393 (2005j:35210)
    • (2004) Dynamics of PDE , vol.1 , pp. 1-48
    • Tao, T.1
  • 78
    • 44849106120 scopus 로고    scopus 로고
    • A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations
    • MR2304091 (2007k:35479).
    • T. Tao, A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations, Dynamics of PDE 4 (2007), 1-53. MR2304091 (2007k:35479)
    • (2007) Dynamics of PDE , vol.4 , pp. 1-53
    • Tao, T.1
  • 79
    • 58649101681 scopus 로고    scopus 로고
    • Nonlinear dispersive equations: local and global analysis, CBMS Regional Series in Mathematics, MR2233925.
    • T. Tao, Nonlinear dispersive equations: local and global analysis, CBMS Regional Series in Mathematics, 2006. MR2233925
    • (2006)
    • Tao, T.1
  • 80
    • 33750606341 scopus 로고    scopus 로고
    • Scattering for the quartic generalised Korteweg-de Vries equation
    • MR2286393.
    • T. Tao, Scattering for the quartic generalised Korteweg-de Vries equation, J. Diff. Eq. 232 (2007), 623-651. MR2286393
    • (2007) J. Diff. Eq. , vol.232 , pp. 623-651
    • Tao, T.1
  • 81
    • 35349001167 scopus 로고    scopus 로고
    • Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in high dimensions
    • MR2355070.
    • T. Tao, M. Visan, and X. Zhang, Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in high dimensions, Duke Math. J., 140 (2007), 165-202. MR2355070
    • (2007) Duke Math. J. , vol.140 , pp. 165-202
    • Tao, T.1    Visan, M.2    Zhang, X.3
  • 82
    • 33747160716 scopus 로고    scopus 로고
    • On the long time behavior of KdV type equations [after Martel-Merle], Séminaire Bourbaki. Astérisque No. 299 (2005), Exp. No. 933, viii, 219-248. MR2167208 (2006g:35246).
    • N. Tzvetkov, On the long time behavior of KdV type equations [after Martel-Merle], Séminaire Bourbaki. Vol. 2003/2004. Astérisque No. 299 (2005), Exp. No. 933, viii, 219-248. MR2167208 (2006g:35246)
    • (2005) , vol.2003-2004 , pp. 219-248
    • Tzvetkov, N.1
  • 83
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • MR691044 (84d:35140).
    • M.I.Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys. 87 (1983), 567-576. MR691044 (84d:35140)
    • (1983) Commun. Math. Phys. , vol.87 , pp. 567-576
    • Weinstein, M.I.1
  • 84
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrodinger equations
    • MR783974 (86i:35130).
    • M. Weinstein, Modulational stability of ground states of nonlinear Schrodinger equations, SIAM J. Math. Anal. 16 (1985), 472-491. MR783974 (86i:35130)
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 472-491
    • Weinstein, M.1
  • 85
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive equations
    • MR820338 (87f:35023).
    • M. Weinstein, Lyapunov stability of ground states of nonlinear dispersive equations, CPAM 39 (1986), 51-68. MR820338 (87f:35023)
    • (1986) CPAM , vol.39 , pp. 51-68
    • Weinstein, M.1
  • 86
    • 33846361348 scopus 로고
    • Interaction of 'Solitons' in a Collisionless Plasma and the Recurrence of Initial States
    • N. J. Zabusky, M. D. Kruskal, Interaction of 'Solitons' in a Collisionless Plasma and the Recurrence of Initial States., Phys. Rev. Lett. 15 (1965), 240.
    • (1965) Phys. Rev. Lett , vol.15 , pp. 240
    • Zabusky, N.J.1    Kruskal, M.D.2
  • 87
    • 0000444166 scopus 로고
    • Asymptotic behavior of non-linear wave systems integrated by the inverse scattering method
    • MR0673411 (58:32546).
    • V.E. Zakharov, S.V. Manakov, Asymptotic behavior of non-linear wave systems integrated by the inverse scattering method, Soviet Physics JETP 44 (1976), 106-112. MR0673411 (58:32546)
    • (1976) Soviet Physics JETP , vol.44 , pp. 106-112
    • Zakharov, V.E.1    Manakov, S.V.2


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