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Variable mesh difference schemes for solving a nonlinear Schrödinger equation with a linear damping term. (English) Zbl 0965.65109
Summary: This paper describes moving variable mesh finite difference schemes to numerically solve the nonlinear Schrödinger equation including the effects of damping and nonhomogeneity in the propagation media. These schemes have accurately predicted the location of the peak of the soliton compared to the uniform mesh, for the case in which the exact solution is known. Numerical results are presented when damping and nonhomogeneous effects are included, and in the absence of these effects the results were verified with the available exact solution.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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