Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4612565 | Journal of Differential Equations | 2007 | 30 Pages |
Abstract
This work is concerned with stability properties of periodic traveling waves solutions of the focusing Schrödinger equationiut+uxx+|u|2u=0iut+uxx+|u|2u=0 posed in RR, and the modified Korteweg–de Vries equationut+3u2ux+uxxx=0ut+3u2ux+uxxx=0 posed in RR. Our principal goal in this paper is the study of positive periodic wave solutions of the equation ϕω″+ϕω3−ωϕω=0, called dnoidal waves. A proof of the existence of a smooth curve of solutions with a fixed fundamental period L , ω∈(2π2/L2,+∞)→ϕω∈Hper∞([0,L]), is given. It is also shown that these solutions are nonlinearly stable in the energy space Hper1([0,L]) and unstable by perturbations with period 2L in the case of the Schrödinger equation.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jaime Angulo Pava,