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Bäcklund autotransformation for the equationu xt=eu−e−2u

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Abstract

The system of differential relations that arises in connection with the Bullough-Dodd-Zhiber-Shabat equationu xt=eu−e−2u is considered. The consistency of this system is established, and it is shown that the system realizes a Bäcklund autotransformation for the equationu xt=eu−e−2u. The associated three-dimensional dynamical systems, which are compatible on a two-dimensional invariant submanifold, are investigated, and a construction of their general solution, which gives the explicit form of the three-parameter soliton for the equationu xt=eu−e−2u, is proposed.

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Authors
  1. S. S. Safin
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  2. R. A. Sharipov
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Additional information

Bashkir State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 146–159, April, 1993.

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Safin, S.S., Sharipov, R.A. Bäcklund autotransformation for the equationu xt=eu−e−2u . Theor Math Phys 95, 462–470 (1993). https://doi.org/10.1007/BF01015902

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  • DOI: https://doi.org/10.1007/BF01015902

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