Reductions and exact solutions of nonlinear multidimensional Schr\"odinger equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 2, pp. 220-234
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Using the canonical decomposition of an arbitrary subalgebra of the orthogonal algebra
$AO(n)$, we describe the maximal subalgebras of rank $n$ and $n-1$ of the extended isochronous Galileo algebra, and also the maximal subalgebras of rank $n$ of the generalized extended classical Galileo algebra $A\widetilde G(1,n)$, the extended special Galileo algebra
$A\widetilde G(2,n)$, and the extended complete Galileo algebra $A\widetilde G(3,n)$. Using the subalgebras of rank $n$, we construct ansatzes that reduce multidimensional Schrödinger
equations to ordinary differential equations. Exact solutions of the Schrödinger equations are found from the solutions of the reduced equations.
@article{TMF_1991_87_2_a4,
author = {A. F. Barannik and V. A. Marchenko and W. I. Fushchych},
title = {Reductions and exact solutions of nonlinear multidimensional {Schr\"odinger} equations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {220--234},
publisher = {mathdoc},
volume = {87},
number = {2},
year = {1991},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1991_87_2_a4/}
}
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A. F. Barannik; V. A. Marchenko; W. I. Fushchych. Reductions and exact solutions of nonlinear multidimensional Schr\"odinger equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 2, pp. 220-234. http://geodesic.mathdoc.fr/item/TMF_1991_87_2_a4/