@Article{JNMA-6-413, author = {Zhang , Hongyi and Zhang , Yufeng}, title = {Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {2}, pages = {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.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.413}, url = {http://global-sci.org/intro/article_detail/jnma/23183.html} }