Olena Vaneeva (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)
Roman Popovych (Wolfgang Pauli Institute, Vienna, Austria & Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

Equivalence transformations in the study of integrability

Abstract:
We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence groupoid of a class of differential equations is described and then specified for the case of evolution equations. A class of fifth-order variable-coefficient KdV-like equations is studied within the framework suggested.

Joint work with Christodoulos Sophocleous, arXiv:1308.5126, invited paper in Physica Scripta.