Exact solutions of the 3-wave resonant interaction equation

A. Degasperis; S. Lombardo

doi:10.1016/j.physd.2006.01.003

Exact solutions of the 3-wave resonant interaction equation

A. Degasperis, S. Lombardo

Mathematics

Research output: Contribution to Journal › Article › Academic › 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
Journal	Physica D. Nonlinear Phenomena
Volume	214
Issue number	2
DOIs	https://doi.org/10.1016/j.physd.2006.01.003
Publication status	Published - 2006

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MR2212247

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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.",

author = "A. Degasperis and S. Lombardo",

note = "MR2212247 ",

year = "2006",

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AU - Lombardo, S.

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N2 - 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.

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.

U2 - 10.1016/j.physd.2006.01.003

DO - 10.1016/j.physd.2006.01.003

M3 - Article

SN - 0167-2789

VL - 214

SP - 157

EP - 168

JO - Physica D. Nonlinear Phenomena

JF - Physica D. Nonlinear Phenomena

IS - 2

ER -

Exact solutions of the 3-wave resonant interaction equation

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