ALGORITHMIC METHOD FOR DERIVING LAX PAIRS FROM THE INVARIANT PAINLEVE ANALYSIS OF NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS

Given a partial differential equation, its Painleve analysis will first be performed with a built-in invariance under the homographic group acting on the singular manifold function. Then, assuming an order for the underlying Lax pair, a multicomponent pseudopotential of projective Riccati type, the components of which are homographically invariant, is introduced. If the equation admits a classical Darboux transformation, a very small set of determining equations whose solution yields the Lax pair will be generated in the basis of the pseudopotential. This new method will be applied to find the yet unpublished Lax pair of the scalar Hirota-Satsuma equation.