Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Instability of the solitary wave solutions for the generalized derivative nonlinear Schrödinger equation in the endpoint case (1804.02738v1)

Published 8 Apr 2018 in math.AP

Abstract: We consider the stability theory of solitary wave solutions for the generalized derivative nonlinear Schr\"odinger equation $$ i\partial_{t}u+\partial_{x}{2}u+i|u|{2\sigma}\partial_x u=0, $$ where $1<\sigma<2$. The equation has a two-parameter family of solitary wave solutions of the form $$ u_{\omega,c}(t,x)=e{i\omega t+i\frac c2(x-ct)-\frac{i}{2\sigma+2}\int_{-\infty}{x-ct}\varphi{2\sigma}{\omega,c}(y)dy}\varphi{\omega,c}(x-ct). $$ The stability theory in the frequency region of $|c|<2\sqrt{\omega}$ was studied previously. In this paper, we prove the instability of the solitary wave solutions in the endpoint case $c=2\sqrt{\omega}$.

Citations (5)

Summary

We haven't generated a summary for this paper yet.