论文信息 - Instability of solitons for the critical generalized Korteweg—de Vries equation

Instability of solitons for the critical generalized Korteweg—de Vries equation

Abstract. We prove in this paper the instability of the solitons for the critical generalized Korteweg—de Vries equation. We obtain this result by a qualitative study of the solution close to the soliton and obtain a large set of initial data giving the instability. This study is a step towards the existence and description of blow up solutions.

Frank Merle | Yvan Martel | F. Merle | Y. Martel

[1] V. Zakharov,et al. Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media , 1970 .

[2] J. Ginibre,et al. Uniqueness of solutions for the generalized Korteweg-de Vries equation , 1989 .

[3] Frank Merle,et al. A Liouville theorem for the critical generalized Korteweg–de Vries equation , 2000 .

[4] J. Shatah,et al. Stability theory of solitary waves in the presence of symmetry, II☆ , 1990 .

[5] I. I. Bakelʹman,et al. Geometric Analysis and Nonlinear Partial Differential Equations , 1993 .

[6] D. Korteweg,et al. XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .

[7] G. Weiss,et al. EIGENFUNCTION EXPANSIONS. Associated with Second-order Differential Equations. Part I. , 1962 .

[8] C. Kenig,et al. Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle , 1993 .

[9] P. Lax. INTEGRALS OF NONLINEAR EQUATIONS OF EVOLUTION AND SOLITARY WAVES. , 1968 .

[10] M. Weinstein. Lyapunov stability of ground states of nonlinear dispersive evolution equations , 1986 .

[11] P. Souganidis,et al. Stability and instability of solitary waves of Korteweg-de Vries type , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.