Asymptotic stability of solitons for subcritical generalized KdV equations

Archive for Rational Mechanics and Analysis

Volumn 157, Issue 3, 2001, Pages 219-254

  Martel, Yvan ^a   Merle, Frank ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035609368     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050100138     Document Type: Article

References (22)

1. J. L. BONA, V. A. DOUGALIS, O. A. KARAKASHIAN & W. R. McKINNEY, Conservative, high order numerical schemes, Phil. Trans. Roy. Soc. London Ser: A. 351, (1995) 107-164.
2. J. L. BONA, P.E. SOUGANIDIS & W. A. STRAUSS, Stability and instability of solitary waves of Korteweg-de Vries type. Proc. R. Soc. Land. 411, (1987) 395-412.
3. J. BOURGAIN. Harmonic analysis and nonlinear partial differential equations, Proceedings of the International Congress of Mathematicians, 1,2, (Zurich, 1994) 31-44. Birkhäuser, Basel, 1995.
4. J. BOURGAIN & W. WANG, Construction of blow up solutions for the nonlinear Schrödinger equation with critical nonlinearity, preprint 97, to appear in Annali Scuola Normale, Pisa (Vol. dedicated to De Giorgi).
5. T. CAZENAVE & P.L. LIONS, Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys. 85, (1982) 549-561.
6. J. GINIBRE & Y. TSUTSUMI, Uniqueness of solutions for the generalized Korteweg-de Vries equation, SIAM J. Math. Anal. 20. (1989) 1388-1425.
7. M. GRILLAKIS, J. SHATAH & W. STRAUSS, Stability theory of solitary waves in the presence of symmetry, J. Funct Anal. 74. (1987) 160-197.
8. T. KATO, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Advances in Mathematical Supplementary Studies, Studies in Applied Math. 8, (1983) 93-128.
9. C. E. KENIG, G. PONCE & 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.
10. C. E. KENIG, G. PONCE & L. VEGA, On the ill posedness of some canonical dispersive equations, preprint.
11. 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.
12. G. L. LAMB JR., Element of soliton theory (John Wiley & Sons, New York 1980).
13. P. D. LAX, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21, (1968) 467-490.
14. Y. MARTEL & F. MERLE, Instability of solitons for the critical generalized Korteweg-de Vries equation, to appear in Geometrical and Functional Analysis.
15. Y. MARTEL & F. MERLE, A Liouville Theorem for the critical generalized Korteweg-de Vries equation, J. Math. Pures Appl. 79, (2000) 339-425.
16. F. MERLE & H. ZAAG, A Liouville Theorem for a vector valued nonlinear heat equation and applications, Math. Annalen 316, (2000) 103-137.
17. R. M. MIURA, The Korteweg-de Vries equation: a survey of results, SIAM Review 18, (1976) 412-459.
18. T. MIZUMACHI, Large time asymptotics of solutions around solitary waves to the generalized Korteweg-de Vries equation, to appear in SIAM J. Math. Anal.
19. R. L. PEGO & M.I. WEINSTEIN. Asymptotic stability of solitary waves, Commun. Math. Phys. 164, (1994) 305-349.
20. E. C. TITCHMARSH, Eigenfunction expansions associated with second-order differential equations, (Oxford, Clarendon Press, 1946).
21. M. I. WEINSTEIN, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16, (1985) 472-491.
22. M. I. WEINSTEIN, Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure. Appl. Math. 39, (1986) 51-68.