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".
Bibliographical noteFunding Information:
1Research supported in part by NSF Grant DMS 98–03154. 2E-mail: email@example.com. NSERC Postdoctoral Fellow. Corresponding author: Enrique Reyes, Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA.
- Boussinesq equation
- Equations describing affine surfaces
- Equations of pseudospherical type
- Formal integrability
- Formal symmetry
- Geometric integrability