Geodesic
Bäcklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 1, pp. 146-159 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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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