Generalized integrable hierarchies and Combescure symmetry transformations
Abstract
Unifying hierarchies of integrable equations are discussed. They are constructed via the generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical meaning, are in fact the symmetry transformations of generalized integrable hierarchies, though the connection with geometry in the general case is not clear. The generalized equation written in terms of invariants of Combescure transformations are the usual integrable equations and their modified partners. The KP  mKP, DS  mDS hierarchies and Darboux system are considered.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 1997
 DOI:
 10.1088/03054470/30/5/022
 arXiv:
 arXiv:solvint/9606007
 Bibcode:
 1997JPhA...30.1591B
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 17 pages, LaTeX