Long-time asymptotics for a fourth-order dispersive nonlinear Schr\"{o}dinger equation with nonzero boundary conditions
Analysis of PDEs
2022-10-25 v2 Exactly Solvable and Integrable Systems
Abstract
In this work, we consider the long-time asymptotics for the Cauchy problem of a fourth-order dispersive nonlinear Schr\"{o}dinger 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 -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 Schr\"{o}dinger equation.
Keywords
Cite
@article{arxiv.2207.07849,
title = {Long-time asymptotics for a fourth-order dispersive nonlinear Schr\"{o}dinger equation with nonzero boundary conditions},
author = {Weiqi Peng and Yong Chen},
journal= {arXiv preprint arXiv:2207.07849},
year = {2022}
}