On the integrability of a class of Monge-Ampere equations


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BRUNELLI J. C. , GÜRSES M., ZHELTUKHIN K.

REVIEWS IN MATHEMATICAL PHYSICS, vol.13, no.4, pp.529-543, 2001 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Review
  • Volume: 13 Issue: 4
  • Publication Date: 2001
  • Doi Number: 10.1142/s0129055x01000764
  • Journal Name: REVIEWS IN MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.529-543

Abstract

We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge-Ampere equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge-Ampere equations. Local as well nonlocal conserved densities are obtained.