
LongTime Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data 

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KeyWord:RiemannHilbert problem, complex mKdV equation, $\bar{\partial}$steepest descent method, longtime 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 longtime 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 RiemannHilbert problem on the basis of the Lax pair and the scattering data. Then the longtime asymptotics of complex mKdV equation is obtained by studying the solution of the RiemannHilbert problem. 


