New solutions of the~Schwarzian Korteweg--de Vries equation in $2{+}1$ dimensions based on weak symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 380-390
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We consider the $(2+1)$-dimensional integrable Schwarzian Korteweg–de Vries
equation. Using weak symmetries, we obtain a system of partial differential
equations in $1+1$ dimensions. Further reductions lead to second-order
ordinary differential equations that provide new solutions expressible in
terms of known functions. These solutions depend on two arbitrary functions
and one arbitrary solution of the Riemann wave equation and cannot be
obtained by classical or nonclassical symmetries. Some of the obtained
solutions of the Schwarzian Korteweg–de Vries equation exhibit a wide variety
of qualitative behaviors; traveling waves and soliton solutions are
among the most interesting.
Keywords:
weak symmetry, partial differential equation, solitary wave.
@article{TMF_2007_151_3_a5,
author = {M. L. Gandarias and M. S. Bruz\'on},
title = {New solutions of {the~Schwarzian} {Korteweg--de} {Vries} equation in $2{+}1$ dimensions based on weak symmetries},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {380--390},
publisher = {mathdoc},
volume = {151},
number = {3},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a5/}
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M. L. Gandarias; M. S. Bruzón. New solutions of the~Schwarzian Korteweg--de Vries equation in $2{+}1$ dimensions based on weak symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 380-390. http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a5/