Toward a classification of quasirational solutions of the nonlinear Schrödinger equation

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.