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arXiv · 0905.4231

Symmetries for exact solutions to the nonlinear Schrödinger equation

Tuncay Aktosun·Theresa Busse·Francesco Demontis·Cornelis van der Mee
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Abstract

A certain symmetry is exploited in expressing exact solutions to the focusing nonlinear Schrödinger equation in terms of a triplet of constant matrices. Consequently, for any number of bound states with any number of multiplicities the corresponding soliton solutions are explicitly written in a compact form in terms of a matrix triplet. Conversely, from such a soliton solution the corresponding transmission coefficients, bound-state poles, bound-state norming constants and Jost solutions for the associated Zakharov-Shabat system are evaluated explicitly. It is also shown that these results hold for the matrix nonlinear Schrödinger equation of any matrix size.

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Tuncay Aktosun, Theresa Busse, Francesco Demontis, Cornelis van der Mee. 2009-05-26. Symmetries for exact solutions to the nonlinear Schrödinger equation. https://doi.org/10.1088/1751-8113%2F43%2F2%2F025202

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