Classical Symmetry Reductions of the Schwarz--Korteweg--de~Vries Equation in $2+1$ Dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 74-84
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Classical reductions of a $(2+1)$-dimensional integrable Schwarz–Korteweg–de Vries equation are classified. These reductions to systems of partial differential equations in $1+1$ dimensions admit symmetries that lead to further reductions, i.e., to systems of ordinary differential equations. All these systems have been reduced to second-order ordinary differential equations. We present some particular solutions involving two arbitrary functions.
Keywords:
partial differential equations, Lie symmetries.
@article{TMF_2003_134_1_a6,
author = {M. L. Gandarias and M. S. Bruz\'on and J. Ram{\'\i}res},
title = {Classical {Symmetry} {Reductions} of the {Schwarz--Korteweg--de~Vries} {Equation} in $2+1$ {Dimensions}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {74--84},
publisher = {mathdoc},
volume = {134},
number = {1},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a6/}
}
TY - JOUR AU - M. L. Gandarias AU - M. S. Bruzón AU - J. Ramíres TI - Classical Symmetry Reductions of the Schwarz--Korteweg--de~Vries Equation in $2+1$ Dimensions JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2003 SP - 74 EP - 84 VL - 134 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a6/ LA - ru ID - TMF_2003_134_1_a6 ER -
%0 Journal Article %A M. L. Gandarias %A M. S. Bruzón %A J. Ramíres %T Classical Symmetry Reductions of the Schwarz--Korteweg--de~Vries Equation in $2+1$ Dimensions %J Teoretičeskaâ i matematičeskaâ fizika %D 2003 %P 74-84 %V 134 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a6/ %G ru %F TMF_2003_134_1_a6
M. L. Gandarias; M. S. Bruzón; J. Ramíres. Classical Symmetry Reductions of the Schwarz--Korteweg--de~Vries Equation in $2+1$ Dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 74-84. http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a6/