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Volumn 20, Issue 2, 2008, Pages 177-218

Refined asymptotics around solitons for gKdV equations

Author keywords

Asymptotic stability; Generalized KdV equation; Soliton

Indexed keywords


EID: 41649103047     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2008.20.177     Document Type: Article
Times cited : (23)

References (21)
  • 1
    • 0020591567 scopus 로고
    • Nonlinear scalar field equations. I. Existence of a ground state
    • H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), 313-345.
    • (1983) Arch. Rational Mech. Anal , vol.82 , pp. 313-345
    • Berestycki, H.1    Lions, P.-L.2
  • 3
    • 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
  • 4
    • 41649105232 scopus 로고    scopus 로고
    • T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Studies in applied mathematics, 93-128, Adv. Math. Suppl. Stud., 8, Academic Press, New York, 1983.
    • T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Studies in applied mathematics, 93-128, Adv. Math. Suppl. Stud., 8, Academic Press, New York, 1983.
  • 5
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • C. E. Kenig, G. Ponce and L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math., 46 (1993), 527-620.
    • (1993) Comm. Pure Appl. Math , vol.46 , pp. 527-620
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 6
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math., 21 (1968), 467-490.
    • (1968) Comm. Pure Appl. Math , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 7
    • 4243069100 scopus 로고    scopus 로고
    • Soliton collisions in the ion acoustic plasma equations
    • Yi Li and D.H. Sattinger, Soliton collisions in the ion acoustic plasma equations, J. Math. Fluid Mech., 1 (1999), 117-130.
    • (1999) J. Math. Fluid Mech , vol.1 , pp. 117-130
    • Li, Y.1    Sattinger, D.H.2
  • 8
    • 27544509563 scopus 로고    scopus 로고
    • Asymptotic N-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations
    • Y. Martel, Asymptotic N-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations, Amer. J. Math., 127 (2005), 1103-1140.
    • (2005) Amer. J. Math , vol.127 , pp. 1103-1140
    • Martel, Y.1
  • 9
    • 34249016378 scopus 로고    scopus 로고
    • Linear problems related to asymptotic stability of solitons of the generalized KdV equations
    • Y. Martel, Linear problems related to asymptotic stability of solitons of the generalized KdV equations, SIAM J. Math. Anal., 38 (2006), 759-781.
    • (2006) SIAM J. Math. Anal , vol.38 , pp. 759-781
    • Martel, Y.1
  • 10
    • 0034164847 scopus 로고    scopus 로고
    • A Liouville theorem for the critical generalized Korteweg-de Vries equation
    • Y. Martel and F. Merle, A Liouville theorem for the critical generalized Korteweg-de Vries equation, J. Math. Pures Appl., 79 (2000), 339-425.
    • (2000) J. Math. Pures Appl , vol.79 , pp. 339-425
    • Martel, Y.1    Merle, F.2
  • 11
    • 0035609368 scopus 로고    scopus 로고
    • Asymptotic stability of solitons for subcritical generalized KdV equations
    • Y. Martel and F. Merle, Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Ration. Mech. Anal., 157 (2001), 219-254.
    • (2001) Arch. Ration. Mech. Anal , vol.157 , pp. 219-254
    • Martel, Y.1    Merle, F.2
  • 12
    • 0036016142 scopus 로고    scopus 로고
    • 2-critical generalized KdV equations
    • 2-critical generalized KdV equations, J. Amer. Math. Soc., 15 (2002), 617-664.
    • (2002) J. Amer. Math. Soc , vol.15 , pp. 617-664
    • Martel, Y.1    Merle, F.2
  • 13
    • 11844251264 scopus 로고    scopus 로고
    • Asymptotic stability of saluons of the subcritical gKdV equations revisited
    • Y. Martel and F. Merle, Asymptotic stability of saluons of the subcritical gKdV equations revisited, Nonlinearity, 18 (2005), 55-80.
    • (2005) Nonlinearity , vol.18 , pp. 55-80
    • Martel, Y.1    Merle, F.2
  • 14
    • 41649092228 scopus 로고    scopus 로고
    • Asymptotic stability of solitons of the gKdV equations with a general nonlinearity
    • to appear in
    • Y. Martel and F. Merle, Asymptotic stability of solitons of the gKdV equations with a general nonlinearity, to appear in Math. Annalen.
    • Math. Annalen
    • Martel, Y.1    Merle, F.2
  • 15
    • 41649092621 scopus 로고    scopus 로고
    • Y. Martel and F. Merle, Description of two soliton collision for the quartic gKdV equation, arXiv:0709.2672v1
    • Y. Martel and F. Merle, Description of two soliton collision for the quartic gKdV equation, arXiv:0709.2672v1
  • 17
    • 0036882736 scopus 로고    scopus 로고
    • Stability and asymptotic stability in the energy space of the sum of N solitons for the subcritical gKdV equations
    • Y. Martel, F. Merle and Tai-Peng Tsai, Stability and asymptotic stability in the energy space of the sum of N solitons for the subcritical gKdV equations, Commun. Math. Phys., 231 (2002), 347-373.
    • (2002) Commun. Math. Phys , vol.231 , pp. 347-373
    • Martel, Y.1    Merle, F.2    Tsai, T.-P.3
  • 18
    • 0016973738 scopus 로고
    • The Korteweg-de Vries equation: A survey of results
    • R. M. Miura, The Korteweg-de Vries equation: a survey of results, SIAM Review, 18 (1976) 412-459.
    • (1976) SIAM Review , vol.18 , pp. 412-459
    • Miura, R.M.1
  • 19
    • 0035538185 scopus 로고    scopus 로고
    • Large time asymptotics of solutions around solitary waves to the generalized Korteweg-de Vries equations
    • T. Mizumachi, Large time asymptotics of solutions around solitary waves to the generalized Korteweg-de Vries equations, SIAM J. Math. Anal., 32 (2001), 1050-1080.
    • (2001) SIAM J. Math. Anal , vol.32 , pp. 1050-1080
    • Mizumachi, T.1
  • 20
    • 21844510556 scopus 로고
    • Asymptotic stability of solitary waves
    • R. L. Pego and M.I. Weinstein, Asymptotic stability of solitary waves, Commun. Math. Phys. 164 (1994), 305-349.
    • (1994) Commun. Math. Phys , vol.164 , pp. 305-349
    • Pego, R.L.1    Weinstein, M.I.2
  • 21
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • M. I. Weinstein, Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math., 39 (1986), 51-68.
    • (1986) Comm. Pure Appl. Math , vol.39 , pp. 51-68
    • Weinstein, M.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.