Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we apply $\overline{\partial}$-steepest descent method to analyze thelong-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-Hilbertproblem on the basis of the Lax pair and the scattering data. Then the long-time asymptotics of complex mKdV equation is obtained by studying thesolution of the Riemann-Hilbert problem.
Keywords: Riemann-Hilbert problem; complex mKdV equation; $\overline{\partial}$-steepest descent method; long-time asymptotics.