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.
|Journal||Advances in Fuzzy Mathematics|
|Publication status||Published - 2020|
CitationYee, T. L. (2020). Explicit construction of Bäcklund transformations for integrable equations using the mirror method. Advances in Fuzzy Mathematics, 15(1), 59-75.
- Bäcklund transformation
- Mirror transformation