Geodesic
Bäcklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 1, pp. 146-159 
S. S. Safin; R. A. Sharipov. Bäcklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 1, pp. 146-159. http://geodesic.mathdoc.fr/item/TMF_1993_95_1_a13/
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     author = {S. S. Safin and R. A. Sharipov},
     title = {B\"acklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {146--159},
     year = {1993},
     volume = {95},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_1_a13/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The system of differential equalities arisen in connection with the Bullough–Dodd–Jiber–Shabat equation $u_{xt}=e^u-e^{-2u}$ is considered. It is shown that this system realizes the differential Bäcklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$. Associated three-dimensional dynamical systems compatible on the two-dimensional invariant submanifold are investigated. Special technique for obtaining their common solutions and the three-parameter soliton of the equation $u_{xt}=e^u-e^{-2u}$ is suggested.

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