English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the stability theory of solitary wave solutions for thegeneralized 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 theform  $$ u_{\omega,c}(t,x)=e^{i\omega t+i\fracc2(x-ct)-\frac{i}{2\sigma+2}\int_{-\infty}^{x-ct}\varphi^{2\sigma}_{\omega,c}(y)dy}\varphi_{\omega,c}(x-ct).  $$  The stability theory in the frequency region of $|c|<2\sqrt{\omega}$ wasstudied previously. In this paper, we prove the instability of the solitarywave solutions in the endpoint case $c=2\sqrt{\omega}$.

Instability of the solitary wave solutions for the generalized derivative nonlinear Schr\"odinger equation in the endpoint case