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Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation

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  • Irfan Mahmood
  • Muhammad Waseem

Abstract

In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the - th form in terms of Wranskian.

Suggested Citation

  • Irfan Mahmood & Muhammad Waseem, 2021. "Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-5, January.
    • Handle: RePEc:hin:jnlamp:8851043
    DOI: 10.1155/2021/8851043
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