On formal integrability of evolution equations and local geometry of surfaces

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

doi:10.1016/S0926-2245(01)00052-3

On formal integrability of evolution equations and local geometry of surfaces

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

Mathematics

Research output: Contribution to journal › Article › peer-review

17 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 language	English (US)
Pages (from-to)	183-199
Number of pages	17
Journal	Differential Geometry and its Application
Volume	15
Issue number	2
DOIs	https://doi.org/10.1016/S0926-2245(01)00052-3
State	Published - 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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title = "On formal integrability of evolution equations and local geometry of surfaces",

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{"}.",

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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.",

year = "2001",

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AU - Foursov, Mikhail V.

AU - Olver, Peter J.

AU - Reyes, Enrique G.

N1 - 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.

PY - 2001/9

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N2 - 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".

AB - 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".

KW - 35Q53

KW - 37K10

KW - 37K25

KW - Boussinesq equation

KW - Equations describing affine surfaces

KW - Equations of pseudospherical type

KW - Formal integrability

KW - Formal symmetry

KW - Geometric integrability

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DO - 10.1016/S0926-2245(01)00052-3

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SN - 0926-2245

VL - 15

SP - 183

EP - 199

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

IS - 2

ER -

On formal integrability of evolution equations and local geometry of surfaces

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Keywords

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