Exact solutions of the 3-wave resonant interaction equation

Antonio Degasperis; Sara Lombardo

doi:10.1016/j.physd.2006.01.003

Exact solutions of the 3-wave resonant interaction equation

Antonio Degasperis
, Sara Lombardo

Research output: Contribution to journal › Article › peer-review

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. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	157-168
Number of pages	11
Journal	Physica D: Nonlinear Phenomena
Volume	214
Issue number	2
DOIs	https://doi.org/10.1016/j.physd.2006.01.003
Publication status	Published - 15 Feb 2006

Keywords

3-wave interaction
Integrable PDEs
Solitons

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10.1016/j.physd.2006.01.003

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title = "Exact solutions of the 3-wave resonant interaction equation",

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. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

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author = "Antonio Degasperis and Sara Lombardo",

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AU - Lombardo, Sara

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AB - 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. © 2006 Elsevier B.V. All rights reserved.

KW - 3-wave interaction

KW - Integrable PDEs

KW - Solitons

U2 - 10.1016/j.physd.2006.01.003

DO - 10.1016/j.physd.2006.01.003

M3 - Article

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VL - 214

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EP - 168

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 2

ER -

Exact solutions of the 3-wave resonant interaction equation

Abstract

Keywords

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