A numerical method for a system of generalized nonlinear Schrödinger equations. (English) Zbl 0599.65085

Chang, Qianshun; Xu, Linbao

J. Comput. Math. 4, 191-199 (1986).

The authors study a new finite difference scheme for the solution of the initial-boundary value problem of some generalized nonlinear Schrödinger equations, which preserve the conservation of energy. This condition is essential for computational efficiency, especially for the soliton computation. One also proves that the method is unconditionally stable and convergent. By using the Galerkin method the authors prove existence and uniqueness of a generalized solution and the convergence of the iteration method to this solution.

Reviewer: S.Sburlan

MSC:

65Z05	Applications to the sciences
65N06	Finite difference methods for boundary value problems involving PDEs
81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q99	Partial differential equations of mathematical physics and other areas of application

Keywords:

nonlinear Schrödinger equations; computational efficiency; soliton; Galerkin method; convergence