A meshless method and stability analysis for the nonlinear Schrödinger equation

Abstract

In this paper, the non-linear Schrödinger (NLS) equation was solved by a meshless method based on the moving least-squares approximation. Single-soliton solution and interaction of two colliding solitons were studied to validate the accuracy of the proposed method. In calculations, different weight functions in which Gaussian and Wendland’s compactly supported functions were used. For the single-soliton solution of NLS equation whose analytical solution was known , error norms and invariants were calculated for two test problems. The obtained results were compared with both each other and some earlier results. Stability analysis of difference equation was done by applying the proposed method for NLS equation.

Notes

No potential conflict of interest was reported by the authors.