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Symplectic methods for the nonlinear Schrödinger equation

Author

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  • Herbst, B.M.
  • Varadi, F.
  • Ablowitz, M.J.

Abstract

Various symplectic discretizations of the nonlinear Schrödinger equation are compared, including one for the integrable discretization due to Ablowitz and Ladik. The numerical experiments are performed with initial values taken near a homoclinic orbit, i.e., in a situation where integrability is crucial. It is shown that symplectic discretizations can sometimes lead to remarkable improvements, and that in even more sensitive situations some of our best numerical schemes fail.

Suggested Citation

  • Herbst, B.M. & Varadi, F. & Ablowitz, M.J., 1994. "Symplectic methods for the nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 37(4), pages 353-369.
    • Handle: RePEc:eee:matcom:v:37:y:1994:i:4:p:353-369
    DOI: 10.1016/0378-4754(94)00024-7
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    Cited by:

    1. Korabel, Nickolay & Zaslavsky, George M., 2007. "Transition to chaos in discrete nonlinear Schrödinger equation with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 223-237.
    2. Aydın, Ayhan, 2009. "Multisymplectic integration of N-coupled nonlinear Schrödinger equation with destabilized periodic wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 735-751.

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