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A quadratic B-spline finite element method for solving nonlinear Schrödinger equation. (English) Zbl 0940.65106

Summary: A numerical solution of the nonlinear Schrödinger (NLS) equation is obtained by using the quadratic B-spline finite element method. Test problems concerning motion, birth and bound states of solitons of the NLS equation are studied to evaluate the method. Results are compared with various numerical methods.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
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