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

  • Musette M
  • Conte R
  • 8


    Mendeley users who have this article in their library.
  • 66


    Citations of this article.


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This new method will be applied to find the yet unpublished Lax pair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.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Get full text


  • M. Musette

  • R. Conte

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free