Pré-Publication, Document De Travail Année : 2011

Families of quasi-rational solutions of the NLS equation as an extension of higher order Peregrine's solutions.

Résumé

We give a family of solutions of the focusing NLS equation as a product of a quotient of two wronskians of order 2N by an exponential. When we perform a special passage to the limit when all the periods tend to infinity, we get a family of solutions depending on 7N+1 parameters. We give explicit representations of solutions for N=1, 2, 3. As particular cases, we recover the so called higher Peregrine's breathers labeled by the positive integer N.
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Dates et versions

hal-00573955 , version 1 (06-03-2011)
hal-00573955 , version 2 (07-04-2011)
hal-00573955 , version 3 (25-09-2011)
hal-00573955 , version 4 (16-09-2012)

Identifiants

  • HAL Id : hal-00573955 , version 1

Citer

Pierre Gaillard. Families of quasi-rational solutions of the NLS equation as an extension of higher order Peregrine's solutions.. 2011. ⟨hal-00573955v1⟩
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