Samples of noncommutative products in certain differential equations

Abstract

A set of associative noncommutative products is considered in different differential equations of the ordinary and partial types. A method of separation of variables is considered for a large set of those systems. The products involved include for example some * products and some products based on Nijenhuis tensors, which are embedded in the differential equations of the Laplace/Poisson, Lax and Schrödinger styles. A comment on the * -products of Reshetikhin-Jambor-Sykora type is also given in relation to * -products of Vey type.