Asymptotic behavior for a new higher-order nonlinear Schrödinger equation

2024/01/12 by Zhang, Hongyi, Zhang, Yufeng, Feng, Binlu
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2401.06458

Abstract

We investigate the Cauchy problem of a new higher-order nonlinear Schrödinger equation (NHNSE) with weighted Sobolev initial data which is derived by ourselves. By applying ∂-steepest descent method, we derive the long-time asymptotics of the NHNSE. Explicit steps are as follows: first of all, based on the spectral analysis of a Lax pair and scattering matrice, the solution of the NHNSE is exhibted through solving the corresponding Riemann-Hilbert problem. Secondly, by applying some properties of the Riemann-Hilbert problem, we obtain the long-time asymptotics of the solution to the NHNSE. As we know that the properties of the NHNSE presented in the paper have not been found in any scholar journals.

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