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 $$L²-class (equations related with special coordinate nets on the Lobachevsky plane $$L²) are discussed. A method of the construction of solutions to one analytic differential equation of $$L²-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.

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Last modified: April 27, 2005