Symplectic and multi-symplectic methods for coupled nonlinear Schrodinger equations with periodic solutions


Aydin A., Karasoezen B.

COMPUTER PHYSICS COMMUNICATIONS, vol.177, no.7, pp.566-583, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 177 Issue: 7
  • Publication Date: 2007
  • Doi Number: 10.1016/j.cpc.2007.05.010
  • Title of Journal : COMPUTER PHYSICS COMMUNICATIONS
  • Page Numbers: pp.566-583
  • Keywords: coupled nonlinear Schrodinger equation, periodic waves, symplectic and multi-symplectic methods, splitting, BACKWARD ERROR ANALYSIS, COLLISION INTERACTIONS, SCHEMES, SOLITONS, INTEGRATORS, STABILITY, EVOLUTION, WAVES

Abstract

We consider for the integration of coupled nonlinear Schrodinger equations with periodic plane wave solutions a splitting method from the class of symplectic integrators and the multi-symplectic six-point scheme which is equivalent to the Preissman scheme. The numerical experiments show that both methods preserve very well the mass, energy and momentum in long-time evolution. The local errors in the energy are computed according to the discretizations in time and space for both methods. Due to its local nature, the multi-symplectic six-point scheme preserves the local invariants more accurately than the symplectic splitting method, but the global errors for conservation laws are almost the same. (C) 2007 Elsevier B.V. All rights reserved.