Symmetry and Integrability of Equations of Mathematical Physics − 2013

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

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.