Correspondence theorems for hierarchies of equations of pseudo-spherical type

2002/12/19 by Enrique G. Reyes, Enríque G. Reyes, Reyes, Enrique G. · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.AP #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0212044

30 pages

arxiv created 2002/12/19 · openalex publication_date 2002/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hierarchies of evolution equations of pseudo-spherical type are introduced, generalizing the notion of a single equation describing pseudo-spherical surfaces due to S.S. Chern 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,\bf R)--valued linear problems. As an application, it is shown that there exists a local correspondence between any two (suitably generic) solutions of arbitrary hierarchies of equations of pseudo-spherical type.

Cited by

• A look on equations describing pseudospherical surfaces
• Global and blow-up solutions for a non-local integrable equation with applications to geometry

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