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Novel Bäcklund Transformations for Integrable Equations

Author

Listed:
  • Pilar Ruiz Gordoa

    (Área de Matemática Aplicada, ESCET Universidad Rey Juan Carlos C, Tulipán s/n, 28933 Móstoles, Madrid, Spain)

  • Andrew Pickering

    (Área de Matemática Aplicada, ESCET Universidad Rey Juan Carlos C, Tulipán s/n, 28933 Móstoles, Madrid, Spain)

Abstract

In this paper, we construct a new matrix partial differential equation having a structure and properties which mirror those of a matrix fourth Painlevé equation recently derived by the current authors. In particular, we show that this matrix equation admits an auto-Bäcklund transformation analogous to that of this matrix fourth Painlevé equation. Such auto-Bäcklund transformations, in appearance similar to those for Painlevé equations, are quite novel, having been little studied in the case of partial differential equations. Our work here shows the importance of the underlying structure of differential equations, whether ordinary or partial, in the derivation of such results. The starting point for the results in this paper is the construction of a new completely integrable equation, namely, an inverse matrix dispersive water wave equation.

Suggested Citation

  • Pilar Ruiz Gordoa & Andrew Pickering, 2022. "Novel Bäcklund Transformations for Integrable Equations," Mathematics, MDPI, vol. 10(19), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3565-:d:929528
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