Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations

  • Musette M
  • Conte R
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Given a partial differential equation, its Painlevé analysis will
first be performed with a builtin 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This new method will be applied to find the yet unpublished Lax pair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.

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  • M. Musette

  • R. Conte

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