SYMPLECTIC NUMERICAL METHODS IN DYNAMICS OF NONLINEAR WAVES

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

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 05, 967-980

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.

Keywords: Symplectic integrators; Integrable equations; Nonlinear Schrödinger equation; Integrals of motion; Modulational instability; Stochastic; Higher-order dispersion; Optical solitons (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000760

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