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Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations. (English) Zbl 0734.35086

Summary: Given a partial differential equation, its Painlevé 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 This new method will be applied to find the yet unpublished Lax pair of the scalar Hirota-Satsuma equation.

MSC:

35Q35 PDEs in connection with fluid mechanics
35A20 Analyticity in context of PDEs
35Q51 Soliton equations
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