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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.

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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