This article is cited in 6 papers

Toward a classification of quasirational solutions of the nonlinear Schrödinger equation

P. Gaillard

Université de Bourgogne, Institut de Mathématiques de Bourgogne, Dijon, France

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. The se 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.

PACS: 33Q55, 37K10, 47.10A-, 47.35.Fg, 47.54.Bd

DOI: 10.4213/tmf9017

 English version: Theoretical and Mathematical Physics, 2016, 189:1, 1440–1449

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