Difference schemes for solving the generalized nonlinear Schrodinger equation

This paper studies finite difference schemes for solving the generalized no nlinear Schrodinger (GNLS) equation iu(t) - u(x)x + q(\u\(2))u = f(x, t)u. A new linearlized Crank-Nicolson-type scheme is presented by applying an ex trapolation technique to the real coefficient of the nonlinear term in the GNLS equation. Several schemes, including Crank-Nicolson-type schemes, Hops cotch-type schemes, split step Fourier scheme, and pseudospectral scheme, a re adopted for solving three model problems of GNLS equation which arise fr om many physical problems. with q(s) = s(2), q(s)= In(1 + s), and q(s)= -4s /(1 + s), respectively. The numerical results demonstrate that the lineariz ed Crank-Nicolson scheme is efficient and robust. (C) 1999 Academic Press.