On the complete integrability of the Hirota-Satsuma system

The authors have applied the Painleve Test to the coupled nonlinear system advocated by Hirota and Satsuma (1981). They have also made a Lie point symmetry analysis of these equations and have shown that the reduced ordinary nonlinear equations are not members of the Painleve class. Also the Painleve test itself is seen to fail, so that on both counts the equations are not completely integrable in the usual sense.