Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

Details Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

2006-04-19

arxiv.org/abs/nlin/0604039v1

J. Phys. A: Math. Gen. 38 (2005) 9649-9663

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, 6 figures

Scientific paper

10.1088/0305-4470/38/44/003

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.

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