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A semi-implicit moving mesh method for the focusing nonlinear Schrödinger equation

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  • An efficient adaptive moving mesh method for investigation of the semi-classical limit of the focusing nonlinear schrödinger equation is presented. The method employs a dynamic mesh to resolve the sea of solitons observed for small dispersion parameters. A second order semi-implicit discretization is used in conjunction with a dynamic mesh generator to achieve a cost-efficient, accurate, and stable adaptive scheme. This method is used to investigate with highly resolved numerics the solution's behavior for small dispersion parameters. Convincing evidence is presented of striking regular space-time patterns for both analytic and non-analytic inital data.
    Mathematics Subject Classification: 35Q55, 65M50.


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