ON THE POSSIBILITY OF EXACT RECIPROCAL TRANSFORMATIONS FOR ONE-SOLITON SOLUTIONS TO EQUATIONS OF THE LOBACHEVSKY CLASS

摘要

Problems on reciprocal transformation of solutions to equations of Λ~2-class (equations related to special coordinate nets on the Lobachevsky plane Λ~2) are discussed. A method of construction of solutions to one analytic differential equation of Λ~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 (MKdV) is obtained. This result confirms the possibility of construction of such transition.