Symmetries for exact solutions to the nonlinear Schrödinger equation

Details Symmetries for exact solutions to the nonlinear Schrödinger equation Symmetries for exact solutions to the nonlinear Schrödinger equation

2009-05-26

arxiv.org/abs/0905.4231v1

Journal of Physics A 43 (2010), 025202 (14 pp).

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1088/1751-8113/43/2/025202

A certain symmetry is exploited in expressing exact solutions to the focusing nonlinear Schr\"odinger 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 Schr\"odinger equation of any matrix size.

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