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Research Article Open access CC BY 4.0

Twenty Two Parameter Deformations of the Twelfth Peregrine Breather Solutions to the NLS Equation

Pierre Gaillard, Mickael Gastineau

Advances in Research · pp. 1–11 · Published 26 Apr 2016

10.9734/AIR/2016/25636

Abstract

The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear Schr¨odinger equation (NLS) with its twenty two real parameters deformations solutions to the NLS equation are explicitly constructed here. New families of quasi-rational solutions of the NLS equation in terms of explicit quotients of polynomials of degree 156 in x and t by a product of an exponential depending on t are obtained. The patterns of the modulus of these solutions in the (x; t) plane, in function of the different parameters are studied in details.

NLS equation wronskians Peregrine breather rogue waves

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Cited by 4

The height of an n th-order fundamental rogue wave for the nonlinear Schrödinger equation

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