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

27 Citations (Scopus)

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.

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 - Feb 2006

Keywords

3-wave interaction
solitons
integrable PDEs

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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.",

keywords = "3-wave interaction, solitons, integrable PDEs",

author = "Antonio Degasperis and Sara Lombardo",

year = "2006",

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doi = "10.1016/j.physd.2006.01.003",

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AU - Degasperis, Antonio

AU - Lombardo, Sara

PY - 2006/2

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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.

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.

KW - 3-wave interaction

KW - solitons

KW - integrable PDEs

UR - https://www.scopus.com/pages/publications/32844470880

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

Abstract

Keywords

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