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Article Dans Une Revue Theoretical and Mathematical Physics Année : 2016

Toward a classification of quasirational solutions of the nonlinear Schrödinger equation

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Résumé

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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Dates et versions

hal-01410258 , version 1 (06-12-2016)

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