Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces

Gong Chen; Jiaqi Liu

Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces

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arxiv 1903.03855 v3 pith:6NO7NXXR submitted 2019-03-09 math.AP

Gong Chen , Jiaqi Liu This is my paper · ORCID

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keywords spacesasymptoticsequationinitialmodifiedsobolevsolutionsweighted

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abstract

The long time behavior of solutions to the defocusing modified Korteweg-de vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift and Zhou and its reformulation by Dieng and McLaughlin through $\overline{\partial}$-derivatives. To extend the asymptotics to solutions with initial data in lower regularity spaces, we apply a global approximation via PDE techniques.

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