Geodesic
Additional symmetries and B\"acklund transformations for the~dispersionless Harry Dym hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 45-57

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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. 
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     author = {Yu.-T. Chen and J.-H. Chang and M. H. Tu},
     title = {Additional symmetries and {B\"acklund} transformations for the~dispersionless {Harry} {Dym} hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {45--57},
     publisher = {mathdoc},
     volume = {152},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a3/}
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Yu.-T. Chen; J.-H. Chang; M. H. Tu. Additional symmetries and B\"acklund transformations for the~dispersionless Harry Dym hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 45-57. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a3/