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2007.152: Exact solutions of the 3-wave resonant interaction equation

2007.152: Antonio Degasperis and Sara Lombardo (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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DOI: 10.1016/j.physd.2006.01.003


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 2003 > 02 Mathematical methods in physics
MIMS number:2007.152
Deposited By:Mrs Louise Healey
Deposited On:16 November 2007

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