Rational solitons of wave resonant-interaction models

Degasperis, Antonio and Lombardo, Sara (2013) Rational solitons of wave resonant-interaction models. Physical Review E, 88 (5). 052914. ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.88.052914


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.

Item Type: Article
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 25 Nov 2013 08:55
Last Modified: 17 Dec 2023 14:52
URI: https://nrl.northumbria.ac.uk/id/eprint/14707

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