A differential quadrature algorithm for nonlinear Schrodinger equation

Korkmaz A., Dag İ.

NONLINEAR DYNAMICS, vol.56, pp.69-83, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56
  • Publication Date: 2009
  • Doi Number: 10.1007/s11071-008-9380-0
  • Journal Name: NONLINEAR DYNAMICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.69-83
  • Keywords: Differential quadrature, Interaction of solitons, Lagrange interpolation polynomials, Nonlinear Schrodinger equation, Solitary waves, DISCRETIZATION METHOD QDM, DISTRIBUTED SYSTEM EQUATIONS, SPLINE FINITE-ELEMENT, PLATES, SOLITON, CONVECTION, INSIGHTS, MEDIA, WAVES, DQ
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

Numerical solutions of a nonlinear Schrodinger equation is obtained using the differential quadrature method based on polynomials for space discretization and Runge-Kutta of order four for time discretization. Five well-known test problems are studied to test the efficiency of the method. For the first two test problems, namely motion of single soliton and interaction of two solitons, numerical results are compared with earlier works. It is shown that results of other test problems agrees the theoretical results. The lowest two conserved quantities and their relative changes are computed for all test examples. In all cases, the differential quadrature Runge-Kutta combination generates numerical results with high accuracy.