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| Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data |
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| KeyWord:Riemann-Hilbert problem, complex mKdV equation, $\bar{\partial}$-steepest descent method, long-time asymptotics |
| Author Name | Affiliation | | Hongyi Zhang | School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China | | Yufeng Zhang | School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China |
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| Abstract: |
| In this paper, we apply $\bar{\partial}$-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. |
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