AN APPLICATION OF GROUP ANALYSIS METHODS TO THE STUDY OF GENERALIZED TODA LATTICES WITH TWO EXPONENTS
Abstract
In the article, we consider the equation y′′=(λ-(1/k) y′2)(k/y+ 2y/(1-x2-y2)) in the semicircle 1-x2-y2>0, y=y(x)>0, kλ>0 , to which the generalized Toda lattices with a Hamiltonian containing two exponents reduce.
For sufficiently small in absolute value λ, this equation can be replaced by a simpler equation setting λ = 0. It is proved that the latter has one-dimensional symmetry group and reduces to a differential first-order equation, by means of which one can get an arbitrarily accurate description of the general solution of the simplified second-order equation near the boundary of the semicircle.
About the Authors
M. V. MILOVANOV
Белорусский государственный педагогический университет, Минск
Belarus
Belarus
O. G. MEDVEDEVA
Белорусский государственный педагогический университет, Минск
Belarus
Belarus
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