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Pré-Publication, Document De Travail Année : 2016

Patterns of deformations of P 3 and P 4 breathers solutions to the NLS equation

Résumé

In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a quotient of two determinants by an exponential depending on t. This formulation gives in the case of the order 3 and 4, solutions with respectively 4 and 6 parameters. With this method, beside Peregrine breathers, we construct all characteristic patterns for the modulus of solutions, like triangular configurations, ring and others.
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Dates et versions

hal-01276394 , version 1 (19-02-2016)

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  • HAL Id : hal-01276394 , version 1

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Pierre Gaillard, Mickaël Gastineau. Patterns of deformations of P 3 and P 4 breathers solutions to the NLS equation. 2016. ⟨hal-01276394⟩
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