Hierarchy of solutions to the NLS equation and multi-rogue waves.

Abstract : The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) are given in terms of determinants. The orders of these determinants are arbitrarily equal to 2N for any nonnegative integer $N$ and generate a hierarchy of solutions which can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N+1) in x and t. These solutions depend on 2N-2 parameters and can be seen as deformations with 2N-2 parameters of the Peregrine breather P_{N} : when all these parameters are equal to 0, we recover the P_{N} breather whose the maximum of the module is equal to 2N+1. Several conjectures about the structure of the solutions are given.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [16 references]  Display  Hide  Download

Contributor : Pierre Gaillard <>
Submitted on : Thursday, July 24, 2014 - 6:36:18 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Tuesday, November 25, 2014 - 5:26:14 PM


Files produced by the author(s)


  • HAL Id : hal-01045243, version 1


Pierre Gaillard. Hierarchy of solutions to the NLS equation and multi-rogue waves.. 2014. ⟨hal-01045243⟩



Record views


Files downloads