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Symplectic Numerical Methods In Dynamics Of Nonlinear Waves

Author

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  • A. G. SHAGALOV

    (Institute of Metal Physics, S.Kovalevskaya 18, GSP-170, Ekaterinburg 620219, Russia)

Abstract

The symplectic integrator of the Gauss–Legendre type is tested on the nonlinear Schrödinger equation. Preservation of high integrals (up to 10 or more) and quasiperiodic motion have been detected for dynamics on both stable soliton and homoclinic manifolds, which indicate applicability of symplectic integrators for adequate simulation of integrable equation. The tested integrator is applied to the problem of long-time stability of the solitons in higher-derivative nonlinear Schrödinger equation. The slow logarithmic-type depletion of the soliton amplitude with time has been detected.

Suggested Citation

  • A. G. Shagalov, 1999. "Symplectic Numerical Methods In Dynamics Of Nonlinear Waves," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 967-980.
    • Handle: RePEc:wsi:ijmpcx:v:10:y:1999:i:05:n:s0129183199000760
    DOI: 10.1142/S0129183199000760
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