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arXiv · 2207.07849

Long-time asymptotics for a fourth-order dispersive nonlinear Schrödinger equation with nonzero boundary conditions

Weiqi Peng·Yong Chen
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Abstract

In this work, we consider the long-time asymptotics for the Cauchy problem of a fourth-order dispersive nonlinear Schrödinger equation with nonzero boundary conditions at infinity. Firstly, in order to construct the basic Riemann-Hilbert problem associated with nonzero boundary conditions, we analysis direct scattering problem. Then we deform the corresponding matrix Riemann-Hilbert problem to explicitly solving models via using the nonlinear steepest descent method and employing the $g$-function mechanism to eliminate the exponential growths of the jump matrices. Finally, we obtain the asymptotic stage of modulation instability for the fourth-order dispersive nonlinear Schrödinger equation.

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Weiqi Peng, Yong Chen. 2022-10-22. Long-time asymptotics for a fourth-order dispersive nonlinear Schrödinger equation with nonzero boundary conditions. https://arxiv.org/abs/2207.07849

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