Traveling-Wave Solutions of the Calogero-Degasperis-Fokas Equation in 2+1 Dimensions |
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Authors: | M L Gandarias S Saez |
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Institution: | (1) Departamento de Matematicas, Universidad de Cadiz, PO Box 40, 11510 Puerto Real, Cadiz, Spain |
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Abstract: | Soliton solutions are among the more interesting solutions of the (2+1)-dimensional integrable Calogero-Degasperis-Fokas (CDF) equation. We previously derived a complete group classiffication for the CDF equation in 2+1 dimensions. Using classical Lie symmetries, we now consider traveling-wave reductions with a variable velocity depending on an arbitrary function. The corresponding solutions of the (2+1)-dimensional equation involve up to three arbitrary smooth functions. The solutions consequently exhibit a rich variety of qualitative behaviors. Choosing the arbitrary functions appropriately, we exhibit solitary waves and bound states.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 44–55, July, 2005. |
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Keywords: | Lie symmetries partial differential equations solitary waves |
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