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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Pogorelov A. V., Differentsialnaya geometriya, Nauka, M., 1974 | MR

[2] Poznyak E. G., Popov A. G., “Geometriya Lobachevskogo i uravneniya matematicheskoi fiziki”, Dokl. RAN, 332:4 (1993), 418–421 | MR | Zbl

[3] Poznyak E. G., Popov A. G., “Geometriya uravneniya $\sin$-Gordona”, Itogi nauki i tekhn. Ser. Probl. geometrii, 23, VINITI, M., 1991, 99–130 | MR

[4] Popov A. G., DAN, 312:5 (1990), 1109–1111 | MR