Efficient and stable numerical methods for the generalized and vector Zakharov system. (English) Zbl 1076.35114

Bao, Weizhu; Sun, Fangfang

SIAM J. Sci. Comput. 26, No. 3, 1057-1088 (2005).

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.

Reviewer: Igor Andrianov (Köln)

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

Keywords:

generalized Zakharov system; NLS; time transverse invariant; subsonic limit; meshing strategy; nonlinear Schrödinger equation; pseudospectral method; Crank-Nicolson scheme