Completely conservative numerical scheme for the nonlinear Schrödinger equation

A. D. Buligin; A. A. Zemlyanov

doi:10.1117/12.2504580

13 December 2018 Completely conservative numerical scheme for the nonlinear Schrödinger equation

A. D. Buligin, A. A. Zemlyanov

Proceedings Volume 10833, 24th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics; 108332J (2018) https://doi.org/10.1117/12.2504580
Event: XXIV International Symposium, Atmospheric and Ocean Optics, Atmospheric Physics, 2018, Tomsk, Russian Federation

Abstract

The fulfillment of the conditions for the complete conservatism of various numerical schemes that are most widely used in the numerical study of the nonlinear Schrödinger equation(NLSE) in the filamentation problem is analyzed, that the use of standard procedures for the numerical realization of NLSE with higher nonlinearities leads to a significant violation of the law of conservation of the Hamilton function in the filamentation process. The solution of this problem is proposed.

Citation Download Citation

A. D. Buligin and A. A. Zemlyanov "Completely conservative numerical scheme for the nonlinear Schrödinger equation", Proc. SPIE 10833, 24th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, 108332J (13 December 2018); https://doi.org/10.1117/12.2504580

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