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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 44–55, July, 2005.
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Gandarias, M.L., Saez, S. Traveling-Wave Solutions of the Calogero-Degasperis-Fokas Equation in 2+1 Dimensions. Theor Math Phys 144, 916–926 (2005). https://doi.org/10.1007/s11232-005-0118-6
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DOI: https://doi.org/10.1007/s11232-005-0118-6