A Meshfree splitting method for soliton dynamics in nonlinear Schrödinger equations
نویسندگان
چکیده
A new method for the numerical simulation of the so-called soliton dynamics arising in a nonlinear Schrödinger equation in the semi-classical regime is proposed. For the time discretization a classical fourth-order splitting method is used. For the spatial discretization, however, a meshfree method is employed in contrast to the usual choice of (pseudo) spectral methods. This approach allows to keep the degrees of freedom almost constant as the semi-classical parameter ε becomes small. This behavior is confirmed by numerical experiments.
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