Rational solitons of wave resonant-interaction models

Antonio Degasperis, Sara Lombardo

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93 Citations (Scopus)
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Abstract

Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations.
Original languageEnglish
Pages (from-to)052914
JournalPhysical Review E
Volume88
Issue number5
DOIs
Publication statusPublished - Nov 2013

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