Generalised symmetries and exact solutions of heat equation

This paper explores the concept of generalised symmetries, particularly those of third and fourth order, which expand the traditional framework of symmetries in the study of partial differential equations (PDEs). Classical symmetries primarily focus on transformations involving the original variables and their first derivatives, generalised symmetries introduce higher-order derivatives as new variables, allowing for a more better understanding of the equation's structure. These higher-order symmetries also facilitate the construction of recursion operators, which systematically generate an infinite sequence of new symmetries from a known one, highlighting a richer integrability structure within PDEs. Moreover, these symmetries may also facilitate the derivation of higher-order conservation laws. In this article, heat equation is discussed for generalised symmetries.