TY - JOUR
T1 - Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data
AU - Zhang , Hongyi
AU - Zhang , Yufeng
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 413
EP - 434
PY - 2024
DA - 2024/06
SN - 6
DO - http://doi.org/10.12150/jnma.2024.413
UR - https://global-sci.org/intro/article_detail/jnma/23183.html
KW - Riemann-Hilbert problem, complex mKdV equation, $\overline{\partial}$-steepest
descent method, long-time asymptotics.
AB - <p style="text-align: justify;">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.</p>