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
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Problems on reciprocal transformation of solutions to equations of
(equations related with
special coordinate nets on the Lobachevsky plane ) are discussed.
A method of the construction of solutions to one analytic
differential equation of -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
Last modified: April 27, 2005