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# 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 Schrodinger 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.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01410258
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 6 décembre 2016 - 15:26:05
Dernière modification le : jeudi 28 janvier 2021 - 10:28:03

### Citation

Pierre Gaillard. Toward a classification of quasirational solutions of the nonlinear Schrödinger equation. Theoretical and Mathematical Physics, Consultants bureau, 2016, 189 (1), pp. 1440-1449 ⟨10.1134/S0040577916100044⟩. ⟨hal-01410258⟩

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