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Theoretical and Mathematical Physics

, Volume 189, Issue 1, pp 1440–1449 | Cite as

Toward a classification of quasirational solutions of the nonlinear Schrödinger equation

  • P. GaillardEmail author
Article

Abstract

Based on a representation in terms of determinants of the order 2N, we attempt to classify quasirational solutions of the one-dimensional focusing nonlinear Schrödinger equation and also formulate several conjectures about the structure of the solutions. These solutions can be written as a product of a t-dependent exponential times a quotient of two N(N+1)th degree polynomials in x and t depending on 2N−2 parameters. It is remarkable that if all parameters are equal to zero in this representation, then we recover the P N breathers.

Keywords

nonlinear Schrödinger equation determinant Peregrine breather rogue wave 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijonFrance

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