On formal integrability of evolution equations and local geometry of surfaces

Mikhail V. Foursov, Peter J. Olver, Enrique G. Reyes

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Some relationships between local differential geometry of surfaces and integrability of evolutionary partial differential equations are studied. It is proven that every second order formally integrable equation describes pseudo-spherical surfaces. A classification of integrable equations of Boussinesq type is presented, and it is shown that they can be interpreted geometrically as "equations describing hyperbolic affine surfaces".

Original languageEnglish (US)
Pages (from-to)183-199
Number of pages17
JournalDifferential Geometry and its Application
Volume15
Issue number2
DOIs
StatePublished - Sep 2001

Bibliographical note

Funding Information:
1Research supported in part by NSF Grant DMS 98–03154. 2E-mail: ereyes@math.ou.edu. NSERC Postdoctoral Fellow. Corresponding author: Enrique Reyes, Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA.

Keywords

  • 35Q53
  • 37K10
  • 37K25
  • Boussinesq equation
  • Equations describing affine surfaces
  • Equations of pseudospherical type
  • Formal integrability
  • Formal symmetry
  • Geometric integrability

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