Traveling-Wave Solutions of the Calogero--Degasperis--Fokas Equation in $2+1$ Dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 44-55
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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.
Keywords:
Lie symmetries, partial differential equations, solitary waves.
@article{TMF_2005_144_1_a4,
author = {M. L. Gandarias and S. Saez},
title = {Traveling-Wave {Solutions} of the {Calogero--Degasperis--Fokas} {Equation} in $2+1$ {Dimensions}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {44--55},
publisher = {mathdoc},
volume = {144},
number = {1},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a4/}
}
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M. L. Gandarias; S. Saez. Traveling-Wave Solutions of the Calogero--Degasperis--Fokas Equation in $2+1$ Dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 44-55. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a4/