Abstract:
Problems on reciprocal transformation of solutions to equations of $\Lambda^2$-class (equations related with special coordinate nets on the Lobachevsky plane $\Lambda^2$) are discussed. A method of the construction of solutions to one analytic differential equation of $\Lambda^2$-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.
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