Exact solutions of the 3-wave resonant interaction equation

Degasperis, Antonio and Lombardo, Sara (2006) Exact solutions of the 3-wave resonant interaction equation. Physica D: Nonlinear Phenomena, 214 (2). pp. 157-168. ISSN 01672789

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Official URL: http://dx.doi.org/10.1016/j.physd.2006.01.003

Abstract

The Darboux–Dressing Transformations are applied to the Lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1+1 dimensions. We display explicit solutions featuring localized waves whose profile vanishes at the spacial boundary |x|=∞, and which are not pure soliton solutions. These solutions depend on an arbitrary function and allow us to deal with collisions of waves with various profiles.

Item Type: Article
Uncontrolled Keywords: 3-wave interaction, solitons, integrable PDEs
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 25 Nov 2013 09:07
Last Modified: 10 Aug 2015 11:34
URI: http://nrl.northumbria.ac.uk/id/eprint/14709

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