Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data

Year:    2024

Author:    Hongyi Zhang, Yufeng Zhang

Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 413–434

Abstract

In this paper, we apply $\overline{\partial}$-steepest descent method to analyze the long-time asymptotics of complex mKdV equation with the initial value belonging to weighted Sobolev spaces. Firstly, the Cauchy problem of the complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering data. Then the long-time asymptotics of complex mKdV equation is obtained by studying the solution of the Riemann-Hilbert problem.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.2024.413

Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 413–434

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Riemann-Hilbert problem complex mKdV equation $\overline{\partial}$-steepest descent method long-time asymptotics.

Author Details

Hongyi Zhang

Yufeng Zhang