Existence of blow-up solutions in the energy space for the critical generalized KdV equation-Reference-Cited by-同舟云学术

Existence of blow-up solutions in the energy space for the critical generalized KdV equation

Published:2001-03-20 Issue:3 Volume:14 Page:555-578
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Merle Frank

Abstract

For the critical generalized Korteweg–de Vries equation, we establish blow-up in finite or infinite time in H 1 ( R ) H^1(\mathbf R) for initial data with negative energy, close to a soliton up to scaling and translation.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2001-14-03/S0894-0347-01-00369-1/S0894-0347-01-00369-1.pdf

Reference28 articles.

1. Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation;Bona, J. L.;Philos. Trans. Roy. Soc. London Ser. A,1995

2. Stability and instability of solitary waves of Korteweg-de Vries type;Bona, J. L.;Proc. Roy. Soc. London Ser. A,1987

3. Harmonic analysis and nonlinear partial differential equations;Bourgain, Jean,1995

4. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations;Bourgain, J.;Geom. Funct. Anal.,1993

5. Orbital stability of standing waves for some nonlinear Schrödinger equations;Cazenave, T.;Comm. Math. Phys.,1982

Cited by 113 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The stability of degenerate solitons for derivative nonlinear Schrödinger equations;Journal of Mathematical Analysis and Applications;2024-11

3. Comparison of different discontinuous Galerkin methods based on various reformulations for gKdV equation: Soliton dynamics and blowup;Computer Physics Communications;2024-07

4. A determination of the blowup solutions to the focusing, quintic NLS with mass equal to the mass of the soliton;Analysis & PDE;2024-06-20

5. Long time asymptotics of large data in the Kadomtsev–Petviashvili models;Nonlinearity;2024-04-02