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Transverse instability for nonlinear Schrödinger equation with a linear potential
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In this article, the transverse instability for a nonlinear Schrodinger equation with a linear potential was considered and the stability of line standing waves was shown for all $L>0.Abstract:
In this paper, we consider the transverse instability for a nonlinear Schrodinger equation with a linear potential on ${\mathbb {R} \times \mathbb {T}_L}$, where $2\pi L$ is the period of the torus $\mathbb{T}_L$. Rose and Weinstein [18] showed the existence of a stable standing wave for a nonlinear Schrodinger equation with a linear potential. We regard the standing wave of nonlinear Schrodinger equation on ${\mathbb R}$ as a line standing wave of nonlinear Schrodinger equation on ${\mathbb R} \times {\mathbb T}_L$. We show the stability of line standing waves for all $L>0$ by using the argument of the previous paper [26].read more
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Stability for line solitary waves of Zakharov-Kuznetsov equation
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Stability for line solitary waves of Zakharov–Kuznetsov equation
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Transverse Stability of Line Soliton and Characterization of Ground State for Wave Guide Schrödinger Equations
TL;DR: In this paper, the transverse stability of the line Schrodinger soliton under a full wave-guide Schroffinger flow on a cylindrical domain was studied, and it was shown that the ground states coincide with the line standing waves.
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Transverse stability of line soliton and characterization of ground state for wave guide Schr\"{o}dinger equations
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