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Efficient and stable numerical methods for the generalized and vector Zakharov system. (English) Zbl 1076.35114
The paper presents stable numerical methods for GZS and vector ZS with and without a linear damping term. The methods are explicit, unconditionally stable, and of spectral-order accuracy in space and second-order accuracy in time. It is based on an time-splitting discretization of a NLS-type equation in GZS; discretizing a nonlinear wave-type equation by a pseudospectral method for spacial derivatives; solving the ODEs in phase space analytically or applying Crank-Nicolson scheme for time derivatives.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65T40 Numerical methods for trigonometric approximation and interpolation
81-08 Computational methods for problems pertaining to quantum theory
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