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, 241 (2). pp. 157-168. ISSN 0167-2789

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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:	PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 02 Mathematical methods in physics
Depositing User:	Ms Lucy van Russelt
Date Deposited:	16 Nov 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/891

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