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Symmetries and Conservation Laws of Kadomtsev—Pogutse Equations

In: Symmetries of Partial Differential Equations

Author

Listed:
  • V. N. Gusyatnikova

    (U.S.S.R. Academy of Sciences, Program Systems Institute)

  • A. V. Samokhin

    (Moscow Institute of Civil Aviation Engineers)

  • V. S. Titov

    (U.S.S.R. Academy of Sciences, Program Systems Institute)

  • A. M. Vinogradov

    (Moscow State University, Department of Mechanics and Mathematics)

  • V. A. Yumaguzhin

    (U.S.S.R. Academy of Sciences, Program Systems Institute)

Abstract

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials ‘in action’. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.

Suggested Citation

  • V. N. Gusyatnikova & A. V. Samokhin & V. S. Titov & A. M. Vinogradov & V. A. Yumaguzhin, 1989. "Symmetries and Conservation Laws of Kadomtsev—Pogutse Equations," Springer Books, in: A. M. Vinogradov (ed.), Symmetries of Partial Differential Equations, pages 23-64, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-1948-8_2
    DOI: 10.1007/978-94-009-1948-8_2
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