Two-dimensional nonlinear equations of the string type and their complete integration
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 323-337
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The general algebraic construction of the authors [1] is used in an investigation of two-dimensional nonlinear dynamical systems associated by a Lax type representation with the local part of an arbitrary graded Lie algebra. These systems contain as simplest case [for simple finite- and infinite-dimensional (of finite growth) Lie algebras] the generalized two-dimensionalized Toda chain. General (in the sense of the Goursat problem) solutions of the equations characterized by the necessary number of arbitrary functions are constructed. Their structure is illustrated by a detailed consideration of “string” type systems associated with a definite embedding of a three-dimensional subalgebra in the algebra $B_n$. The geometrical interpretation of the corresponding equations is discussed.
@article{TMF_1983_54_3_a0,
author = {A. N. Leznov and M. V. Saveliev},
title = {Two-dimensional nonlinear equations of the string type and their complete integration},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {323--337},
publisher = {mathdoc},
volume = {54},
number = {3},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a0/}
}
TY - JOUR AU - A. N. Leznov AU - M. V. Saveliev TI - Two-dimensional nonlinear equations of the string type and their complete integration JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1983 SP - 323 EP - 337 VL - 54 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a0/ LA - ru ID - TMF_1983_54_3_a0 ER -
%0 Journal Article %A A. N. Leznov %A M. V. Saveliev %T Two-dimensional nonlinear equations of the string type and their complete integration %J Teoretičeskaâ i matematičeskaâ fizika %D 1983 %P 323-337 %V 54 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a0/ %G ru %F TMF_1983_54_3_a0
A. N. Leznov; M. V. Saveliev. Two-dimensional nonlinear equations of the string type and their complete integration. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 323-337. http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a0/