The Calogero--Bogoyavlenskii--Schiff Equation in $2+1$ Dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 14-26
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We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the $(2+1)$-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this $(2+1)$-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the
$(2+1)$-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.
Keywords:
partial differential equations, symmetries.
@article{TMF_2003_137_1_a2,
author = {M. S. Bruz\'on and M. L. Gandarias and C. Muriel and J. Ram{\'\i}res and S. Saez and F. R. Romero},
title = {The {Calogero--Bogoyavlenskii--Schiff} {Equation} in $2+1$ {Dimensions}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {14--26},
publisher = {mathdoc},
volume = {137},
number = {1},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a2/}
}
TY - JOUR AU - M. S. Bruzón AU - M. L. Gandarias AU - C. Muriel AU - J. Ramíres AU - S. Saez AU - F. R. Romero TI - The Calogero--Bogoyavlenskii--Schiff Equation in $2+1$ Dimensions JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2003 SP - 14 EP - 26 VL - 137 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a2/ LA - ru ID - TMF_2003_137_1_a2 ER -
%0 Journal Article %A M. S. Bruzón %A M. L. Gandarias %A C. Muriel %A J. Ramíres %A S. Saez %A F. R. Romero %T The Calogero--Bogoyavlenskii--Schiff Equation in $2+1$ Dimensions %J Teoretičeskaâ i matematičeskaâ fizika %D 2003 %P 14-26 %V 137 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a2/ %G ru %F TMF_2003_137_1_a2
M. S. Bruzón; M. L. Gandarias; C. Muriel; J. Ramíres; S. Saez; F. R. Romero. The Calogero--Bogoyavlenskii--Schiff Equation in $2+1$ Dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 14-26. http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a2/