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arXiv · 1407.7974

On a periodic solution of the focusing nonlinear Schrödinger equation

A. O. Smirnov·E. G. Semenova·V. Zinger·N. Zinger
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Abstract

A periodic two-phase algebro-geometric solution of the focusing nonlinear Schrödinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is investigated. An existence of a real smooth finite-gap solution of NLS equation with complex initial phase is proven. Degenerations of the constructed solution to one-phase traveling wave solution and solutions in the form of the plane waves are carried.

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A. O. Smirnov, E. G. Semenova, V. Zinger, N. Zinger. 2014-07-30. On a periodic solution of the focusing nonlinear Schrödinger equation. https://arxiv.org/abs/1407.7974

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