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arXiv · 1705.05974

New integrable semi-discretizations of the coupled nonlinear Schrodinger equations

Sylvie A. Bronsard·Dmitry E. Pelinovsky
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Abstract

We have undertaken an algorithmic search for new integrable semi-discretizations of physically relevant nonlinear partial differential equations. The search is performed by using a compatibility condition for the discrete Lax operators and symbolic computations. We have discovered a new integrable system of coupled nonlinear Schrodinger equations which combines elements of the Ablowitz-Ladik lattice and the triangular-lattice ribbon studied by Vakhnenko. We show that the continuum limit of the new integrable system is given by uncoupled complex modified Korteweg-de Vries equations and uncoupled nonlinear Schrodinger equations.

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Sylvie A. Bronsard, Dmitry E. Pelinovsky. 2017-05-17. New integrable semi-discretizations of the coupled nonlinear Schrodinger equations. https://arxiv.org/abs/1705.05974

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