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Volumn 16, Issue 3, 2003, Pages 929-961

Geometric theory for multi-bump, self-similar, blowup solutions of the cubic nonlinear Schrödinger equation

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EID: 0242277031     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/3/308     Document Type: Article
Times cited : (17)

References (38)
  • 2
    • 0036304184 scopus 로고    scopus 로고
    • Asymptotics of multi-bump blow-up self-similar solutions of the nonlinear Schrödinger equation
    • Budd C J 2002 Asymptotics of multi-bump blow-up self-similar solutions of the nonlinear Schrödinger equation SIAM J. Appl. Math. 62 801-30
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 801-830
    • Budd, C.J.1
  • 3
    • 0001689908 scopus 로고    scopus 로고
    • New self-similar solutions of the nonlinear Schrödinger equation with moving mesh computations
    • Budd C J, Chen S and Russell R D 1999 New self-similar solutions of the nonlinear Schrödinger equation with moving mesh computations J. Comp. Phys. 152 756-89
    • (1999) J. Comp. Phys. , vol.152 , pp. 756-789
    • Budd, C.J.1    Chen, S.2    Russell, R.D.3
  • 5
    • 0242376125 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation as both a PDE and a dynamical system
    • ed B Fiedler (Amsterdam: North-Holland)
    • Cai D, McLaughlin D W and McLaughlin K T R 2002 The nonlinear Schrödinger equation as both a PDE and a dynamical system Handbook of Dynamical Systems, Towards Applications vol 2, ed B Fiedler (Amsterdam: North-Holland) pp 599-675
    • (2002) Handbook of Dynamical Systems, towards Applications , vol.2 , pp. 599-675
    • Cai, D.1    McLaughlin, D.W.2    McLaughlin, K.T.R.3
  • 7
    • 0015249887 scopus 로고
    • 3 = 0 and a variational characterization of other solutions
    • 3 = 0 and a variational characterization of other solutions Arch. Ration. Mech. Anal. 46 81-95
    • (1972) Arch. Ration. Mech. Anal. , vol.46 , pp. 81-95
    • Coffman, C.V.1
  • 8
    • 0000468351 scopus 로고    scopus 로고
    • Homoclinic saddle-node bifurcations in singularly perturbed systems
    • Doelman A and Hek G 2000 Homoclinic saddle-node bifurcations in singularly perturbed systems J. Dyn. Diff. Eqns 12 169-216
    • (2000) J. Dyn. Diff. Eqns , vol.12 , pp. 169-216
    • Doelman, A.1    Hek, G.2
  • 10
    • 0009268172 scopus 로고    scopus 로고
    • Singularly perturbed and non-local modulation equations for systems with interacting instability mechanisms
    • Doelman A and Rottschäfer V 1997 Singularly perturbed and non-local modulation equations for systems with interacting instability mechanisms J. Nonlinear Sci. 7 371-409
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 371-409
    • Doelman, A.1    Rottschäfer, V.2
  • 11
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • Fenichel N 1979 Geometric singular perturbation theory for ordinary differential equations J. Diff. Eqns 31 53-98
    • (1979) J. Diff. Eqns , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 12
    • 0000567112 scopus 로고    scopus 로고
    • Adiabatic law for self-focusing of optical beams
    • Fibich G 1996 Adiabatic law for self-focusing of optical beams Opt. Lett. 21 1735-7
    • (1996) Opt. Lett. , vol.21 , pp. 1735-1737
    • Fibich, G.1
  • 13
    • 0000612727 scopus 로고
    • On the blowing up of the solutions to the Cauchy problem for nonlinear Schrödinger equations
    • Glassey R T 1977 On the blowing up of the solutions to the Cauchy problem for nonlinear Schrödinger equations J. Math. Phys. 18 1974-7
    • (1977) J. Math. Phys. , vol.18 , pp. 1974-1977
    • Glassey, R.T.1
  • 16
    • 20244383864 scopus 로고    scopus 로고
    • Homoclinic orbits and chaos in three- and four-dimensional flows
    • Holmes P, Doelman A, Hek G and Domokos G 2000 Homoclinic orbits and chaos in three- and four-dimensional flows Phil. Trans. R. Soc. A 359 1429-38
    • (2000) Phil. Trans. R. Soc. A , vol.359 , pp. 1429-1438
    • Holmes, P.1    Doelman, A.2    Hek, G.3    Domokos, G.4
  • 18
    • 0030528987 scopus 로고    scopus 로고
    • Tracking invariant manifolds up to exponentially small errors
    • Jones C K R T, Kaper T J and Kopell N 1996 Tracking invariant manifolds up to exponentially small errors SIAM J. Math. Anal. 27 558-77
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 558-577
    • Jones, C.K.R.T.1    Kaper, T.J.2    Kopell, N.3
  • 19
    • 20244362950 scopus 로고    scopus 로고
    • Generalized exchange lemmas and orbits heteroclinic to invariant manifolds
    • submitted
    • Jones C K R T and Tin S K 2002 Generalized exchange lemmas and orbits heteroclinic to invariant manifolds Mem. AMS submitted
    • (2002) Mem. AMS
    • Jones, C.K.R.T.1    Tin, S.K.2
  • 21
    • 33646903221 scopus 로고
    • A geometric criterion for adiabatic chaos
    • Kaper T J and Kovacic G 1994 A geometric criterion for adiabatic chaos J. Math. Phys. 35 1202-18
    • (1994) J. Math. Phys. , vol.35 , pp. 1202-1218
    • Kaper, T.J.1    Kovacic, G.2
  • 22
    • 0040719385 scopus 로고    scopus 로고
    • Multi-bump orbits homoclinic to resonance bands
    • Kaper T J and Kovacic G 1996 Multi-bump orbits homoclinic to resonance bands Trans. Am. Math. Soc. 348 3835-87
    • (1996) Trans. Am. Math. Soc. , vol.348 , pp. 3835-3887
    • Kaper, T.J.1    Kovacic, G.2
  • 23
    • 0029394002 scopus 로고
    • Spatial structure of focusing singularity of the nonlinear Schrödinger equation: A geometrical analysis
    • Kopell N and Landman M 1995 Spatial structure of focusing singularity of the nonlinear Schrödinger equation: a geometrical analysis SIAM J. Appl Math. 55 1297-323
    • (1995) SIAM J. Appl Math. , vol.55 , pp. 1297-1323
    • Kopell, N.1    Landman, M.2
  • 24
    • 44949272407 scopus 로고
    • Computer simulation of wave collapses in the nonlinear Schrödinger equation
    • Kosmatov N E, Shvets V F and Zakharov V E 1991 Computer simulation of wave collapses in the nonlinear Schrödinger equation Physica D 52 16-35
    • (1991) Physica D , vol.52 , pp. 16-35
    • Kosmatov, N.E.1    Shvets, V.F.2    Zakharov, V.E.3
  • 25
    • 0000893351 scopus 로고
    • Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
    • Landman M J, Papanicolaou G C, Sulem C and Sulem P L 1988 Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension Phys. Rev. A 38 3837-43
    • (1988) Phys. Rev. A , vol.38 , pp. 3837-3843
    • Landman, M.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4
  • 26
    • 0001678668 scopus 로고
    • Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
    • Le Mesurier B J, Papanicolaou G C, Sulem C and Sulem P L 1988 Local structure of the self-focusing singularity of the nonlinear Schrödinger equation Physica D 32 210-26
    • (1988) Physica D , vol.32 , pp. 210-226
    • Le Mesurier, B.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4
  • 27
    • 45549111243 scopus 로고
    • Focusing and multi-focusing solutions of the nonlinear Schrödinger equation
    • Le Mesurier B J, Papanicolaou G C, Sulem C and Sulem P L 1986 Focusing and multi-focusing solutions of the nonlinear Schrödinger equation Physica D 31 78-102
    • (1986) Physica D , vol.31 , pp. 78-102
    • Le Mesurier, B.J.1    Papanicolaou, G.C.2    Sulem, C.3    Sulem, P.L.4
  • 29
    • 0000259445 scopus 로고
    • Uniqueness of solutions of semilinear Poisson equations
    • McLeod K and Serrin J 1981 Uniqueness of solutions of semilinear Poisson equations Proc. Natl Acad. Sci. 78 6592-5
    • (1981) Proc. Natl Acad. Sci. , vol.78 , pp. 6592-6595
    • McLeod, K.1    Serrin, J.2
  • 30
    • 4243124914 scopus 로고
    • Passage through a separatrix in a resonance problem with a slowly varying parameter
    • Neihstadt A I 1975 Passage through a separatrix in a resonance problem with a slowly varying parameter PMM 39 594-605
    • (1975) PMM , vol.39 , pp. 594-605
    • Neihstadt, A.I.1
  • 32
    • 0035613474 scopus 로고    scopus 로고
    • On self-similar singular solutions of the complex Ginzburg-Landau equation
    • Plecháč P and Šverák V 2001 On self-similar singular solutions of the complex Ginzburg-Landau equation Commun. Pure Appl. Math. 54 1215-42
    • (2001) Commun. Pure Appl. Math. , vol.54 , pp. 1215-1242
    • Plecháč, P.1    Šverák, V.2
  • 33
    • 84956263763 scopus 로고
    • Blowup in nonlinear Schrödinger equations 1. A general review and 2. Similarity structure of the blowup singularity
    • Rasmussen J J and Rypdal K 1986 Blowup in nonlinear Schrödinger equations 1. A general review and 2. Similarity structure of the blowup singularity Phys. Scr. 33 481-504
    • (1986) Phys. Scr. , vol.33 , pp. 481-504
    • Rasmussen, J.J.1    Rypdal, K.2
  • 34
    • 0002937879 scopus 로고
    • Sustained resonance for a nonlinear system with slowly varying coefficients
    • Robinson C 1983 Sustained resonance for a nonlinear system with slowly varying coefficients SIAM J. Math. Anal. 14 847-960
    • (1983) SIAM J. Math. Anal. , vol.14 , pp. 847-960
    • Robinson, C.1
  • 35
    • 0037091782 scopus 로고    scopus 로고
    • Blowup in the nonlinear Schrödinger equation near critical dimension
    • Rottschäfer V and Kaper T 2002 Blowup in the nonlinear Schrödinger equation near critical dimension J. Math. Anal. Appl. 268 517-49
    • (2002) J. Math. Anal. Appl. , vol.268 , pp. 517-549
    • Rottschäfer, V.1    Kaper, T.2
  • 37
    • 0001906184 scopus 로고
    • Collapse and self-focusing of Langmuir waves
    • general ed M N Rosenbluth
    • Zakharov V E 1984 Collapse and self-focusing of Langmuir waves Handbook of Plasma Physics vol 2 (general) ed M N Rosenbluth and R Z Sagdeev Basic Plasma Physics II ed A A Galeev and R N Sudan (Amsterdam: Elsevier)pp 81-121
    • (1984) Handbook of Plasma Physics , vol.2
    • Zakharov, V.E.1
  • 38
    • 20244363670 scopus 로고    scopus 로고
    • ed A A Galeev and R N Sudan (Amsterdam: Elsevier)
    • Zakharov V E 1984 Collapse and self-focusing of Langmuir waves Handbook of Plasma Physics vol 2 (general) ed M N Rosenbluth and R Z Sagdeev Basic Plasma Physics II ed A A Galeev and R N Sudan (Amsterdam: Elsevier)pp 81-121
    • Basic Plasma Physics II , pp. 81-121
    • Sagdeev, R.Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.