FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 1, PAGES 241-246

**On the possibility of exact reciprocal transformations for one-soliton
solutions to equations of the Lobachevsky class**

M.
S.
Ratinsky

Abstract

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Problems on reciprocal transformation of solutions to equations of
$$L^{2}-class
(equations related with
special coordinate nets on the Lobachevsky plane $$L^{2}) are discussed.
A method of the construction of solutions to one analytic
differential equation of $$L^{2}-class by
a given solution of another analytic differential equation of
this class is proposed.
The reciprocal transformation of one-soliton solutions of the
sine-Gordon equation and one-soliton solutions of the modified
Korteweg--de Vries equation is obtained.
This result confirms the possibility of the construction of such
transition.

Location: http://mech.math.msu.su/~fpm/eng/k05/k051/k05112h.htm

Last modified: April 27, 2005