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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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.
| Item Type: | Article |
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| 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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