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On the integrability of a class of Monge-Ampere equations

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2001-04-01
BRUNELLI, J C
GÜRSES, METİN
Zheltukhın, Kostyantyn
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.