Geodesic
On the possibility of exact reciprocal transformations for one-soliton solutions to equations of the Lobachevsky class
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 241-246

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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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     author = {M. S. Ratinsky},
     title = {On the possibility of exact reciprocal transformations for one-soliton solutions to equations of the {Lobachevsky} class},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {241--246},
     publisher = {mathdoc},
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     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a11/}
}
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M. S. Ratinsky. On the possibility of exact reciprocal transformations for one-soliton solutions to equations of the Lobachevsky class. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 241-246. http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a11/