Spectral analysis and long-time asymptotics of complex mKdV equation
Exactly Solvable and Integrable Systems
2022-03-02 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
In this paper, we obtain the long-time asymptotics of complex mKdV equation via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem of complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering matrix. After that Riemann-Hilbert problems are converted through a decomposition of the matrix-valued spectral function and factorizations of the jump matrix for Riemann-Hilbert problem. Finally, by solving the last model problem, the long-time asymptotics of complex mKdV equation are derived.
Keywords
Cite
@article{arxiv.2110.08763,
title = {Spectral analysis and long-time asymptotics of complex mKdV equation},
author = {Hong-Yi Zhang and Yu-Feng Zhang},
journal= {arXiv preprint arXiv:2110.08763},
year = {2022}
}