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.