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Bäcklund transformations of solutions of nonlinear evolution equations and the Lie Bianchi transformation

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  • de Jager em, E.M.
  • Spannenburg, S.
  • Sitters, M.H.

Abstract

Using the Maurer Cartan structural equations of the Lie group SL(2, R) it is shown that the auto-Bäcklund transformations of solutions of the Sine Gordon, the Korteweg—de Vries and the modified Korteweg—de Vries equation can be derived from the same Lie Bianchi transformation sending surfaces of constant negative curvature into surfaces of the same constant negative curvature.

Suggested Citation

  • de Jager em, E.M. & Spannenburg, S. & Sitters, M.H., 1996. "Bäcklund transformations of solutions of nonlinear evolution equations and the Lie Bianchi transformation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 126-149.
    • Handle: RePEc:eee:phsmap:v:228:y:1996:i:1:p:126-149
    DOI: 10.1016/0378-4371(95)00437-8
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    Cited by:

    1. Gokan, Toshitaka & Kichko, Sergey & Thisse, Jacques-François, 2019. "How do trade and communication costs shape the spatial organization of firms?," Journal of Urban Economics, Elsevier, vol. 113(C).

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