This article is cited in 1 paper

Additional symmetries and Bäcklund transformations for the dispersionless Harry Dym hierarchy

Yu.-T. Chen^a, J.-H. Chang^b, M. H. Tu<sup>c

a</sup> Institute of Mathematics, Academia Sinica
^b National Defense University, Department of Electrical Engineering
^c National Chung Cheng University

Abstract: We give a dispersionless Toda-like extension to the dispersionless Harry Dym (dDym) hierarchy. The extended dDym (EdDym) hierarchy has a dressing formulation, and its underlying solution structure can be investigated through the twistor construction. We show that additional symmetries of the solution space generate Bäcklund transformations of the EdDym hierarchy. We present some examples of constructing new solutions of the $(2+1)$-dimensional dDym and EdDym equations via Bäcklund transformations.

Keywords: dispersionless Dym hierarchy, dressing operator, twistor construction, additional symmetries, Bäcklund transformation.

DOI: 10.4213/tmf6069

 English version: Theoretical and Mathematical Physics, 2007, 152:1, 915–925

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