Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 225, Issue 1, Pages 26-56Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2006.02.007
Keywords
equations of pseudo-spherical type; pseudo-spherical surfaces; Backlund transformations; integrable equations; hierarchies of pseudo-spherical type; generalized symmetries
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Hierarchies of evolution equations of pseudo-spherical type are introduced, thereby generalizing the notion of a single equation describing pseudo-spherical surfaces due to S.S. Chem and K. Tenenblat, and providing a connection between differential geometry and the study of hierarchies of equations which are the integrability condition of sl (2, R)-valued linear problems. As an application, it is shown that there exist local correspondences between any two (suitably generic) solutions of arbitrary hierarchies of equations of pseudo-spherical type. (c) 2006 Elsevier Inc. All rights reserved.
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