On the possibility of exact reciprocal transformations for one-soliton solutions to equations of the Lobachevsky class |
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Authors: | M S Ratinsky |
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Institution: | (1) Moscow State University, Russia |
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Abstract: | Problems on reciprocal transformation of solutions to equations of Λ2-class (equations related to special coordinate nets on the Lobachevsky plane Λ2) are discussed. A method of construction of solutions to one analytic differential equation of Λ2-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
(MKdV) is obtained. This result confirms the possibility of construction of such transition.
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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry,
2005. |
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