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- W2791396759 abstract "We study the stability theory of solitary wave solutions for the generalized derivative nonlinear Schrodinger equation $$ ipartial_{t}u+partial_{x}^{2}u+i|u|^{2sigma}partial_x u=0. $$ The equation has a two-parameter family of solitary wave solutions of the form begin{align*} phi_{omega,c}(x)=varphi_{omega,c}(x)exp{big{ ifrac c2 x-frac{i}{2sigma+2}int_{-infty}^{x}varphi^{2sigma}_{omega,c}(y)dybig}}. end{align*} Here $ varphi_{omega,c}$ is some real-valued function. It was proved in cite{LiSiSu1} that the solitary wave solutions are stable if $-2sqrt{omega }<c <2z_0sqrt{omega }$, and unstable if $2z_0sqrt{omega }<c <2sqrt{omega }$ for some $z_0in(0,1)$. We prove the instability at the borderline case $c =2z_0sqrt{omega }$ for $1<sigma<2$, improving the previous results in cite{Fu-16-DNLS} where $3/2<sigma<2$." @default.
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- W2791396759 date "2018-03-20" @default.
- W2791396759 modified "2023-10-17" @default.
- W2791396759 title "Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrodinger equation in the critical frequency case" @default.
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- W2791396759 doi "https://doi.org/10.48550/arxiv.1803.07700" @default.
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