Periodic and solitary wave solutions of the three-wave problem. A different approach |
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Authors: | A Roy Chowdhury M Debnath R S Banerjee |
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Institution: | (1) High Energy Physics Division, Physics Department, Jadavpur University, 700 032 Calcutta, India |
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Abstract: | We consider the inverse problem for a three-wave interaction system in a manner different from Zakharovet al. and of Kaup. Our method is an adaptation of the technique due to Date to a 3 × 3 Lax pair. The analysis leads to a system of ordinary nonlinear equations for the
ivariables linearizable through a suitable definition of differential on a Riemann surface. Next, in the degenerate case, when the
iare equal in pairs, we prove that such a set of equations is exactly integrable and leads to solitary solutions. |
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Keywords: | |
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