Explicit construction of Bäcklund transformations for integrable equations using the mirror method

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Abstract

A direct and algorithmic method was developed to study the integrability of nonlinear differential equations. The existence of regular mirror systems near movable singularities is guaranteed for integrable equations. We apply this methodology, with suitable modifications, to construct the linearized mirror systems which can naturally lead to the Bäcklund transformations (BTs). The mirror method is used to obtain the BTs of three classical integrable equations such as the Schlesinger transformations of the second Painleve equation. Copyright © 2020 Research India Publications.
Original languageEnglish
Pages (from-to)59-75
JournalAdvances in Fuzzy Mathematics
Volume15
Issue number1
Publication statusPublished - 2020

Citation

Yee, T. L. (2020). Explicit construction of Bäcklund transformations for integrable equations using the mirror method. Advances in Fuzzy Mathematics, 15(1), 59-75.

Keywords

  • Bäcklund transformation
  • Integrability
  • Mirror transformation

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