Numerical Simulation of Coupled Nonlinear Schrödinger Equations Using the Generalized Differential Quadrature Method

Abstract

We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrödinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.

Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

“…In recent years, a great deal of literature gives various numerical schemes for solving the CNLS equations, most of them use the finite difference schemes. [6−8] There are also other numerical methods applied to the CNLS equations, for example, Ismail derived a finite element scheme to solve the equation, [9] Cheng proposed a direct perturbation method, [10] Mokhtari studied the generalized differential quadrature method, [11] Utsumi studied the CIPbasis set method. [12] The multi-symplectic methods can also be applied to the CNLS system.…”

Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

“…[31] Some recent applications of the method can be found in Refs. [5,[32][33][34][35] and references cited therein.…”