Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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{\textendash}Korteweg{\textendash}de~Vries} {Equation} in $2+1$ {Dimensions}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {74--84},
     year = {2003},
     volume = {134},
     number = {1},
     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
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
%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/

[1] K. Toda, S. Yu, J. Math. Phys., 41 (2000), 4747 | DOI | MR | Zbl

[2] F. Calogero, Lett. Nuovo Cimento, 14 (1975), 43 | MR

[3] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[4] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[5] B. Champagne, W. Hereman, P. Winternitz, Comp. Phys. Comm., 66 (1991), 319 | DOI | MR | Zbl

[6] E. L. Ains, Obyknovennye differentsialnye uravneniya, DNTVU, Kharkov, 1939 | MR