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Action as an invariant of Bäcklund transformations for Lagrangian systems

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Abstract

We construct a general theory of Bäcklund transformations for Lagrangian systems under the condition that the action is preserved by these transformations. We discuss the known Bäcklund transformations for classical soliton equations from the standpoint of this approach and obtain a new Bäcklund transformation for the Tzitzéica equation.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Moscow, Russia

    V. G. Marikhin

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  1. V. G. Marikhin
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Correspondence to V. G. Marikhin.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 1, pp. 71–78, July, 2015.

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Marikhin, V.G. Action as an invariant of Bäcklund transformations for Lagrangian systems. Theor Math Phys 184, 953–960 (2015). https://doi.org/10.1007/s11232-015-0308-9

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  • DOI: https://doi.org/10.1007/s11232-015-0308-9

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