ON THE INTEGRABILITY OF A 3RD-ORDER MONGE-AMPERE TYPE EQUATION

A third-order equation, similar to a Monge-Ampere equation, is studied , this being achieved by first converting the equation to a 3 x 3-hydr odynamics system. A Lax pair for this hydrodynamic system is construct ed and the integrability of this system established. In the degenerate case the equations reduce to a simpler integrable hydrodynamic equati on and this case is also studied. The interpretation of this equation as a higher-order Monge-Ampere equation leads to various generalizatio ns which are discussed briefly.