Title: Generalised symmetries and exact solutions of heat equation

Authors: Jaskiran Kaur; Mukesh Sarangal; Manjit Singh

Addresses: Department of Mathematics, Maharaja Ranjit Singh Punjab Technical University, Bathinda – 151001, Punjab, India ' Department of Mathematics, Maharaja Ranjit Singh Punjab Technical University, Bathinda – 151001, Punjab, India ' Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo 151302, Punjab, India

Abstract: 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.

Keywords: exact solutions; generalised symmetries; heat equation.

DOI: 10.1504/IJDSDE.2024.145224

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.5, pp.454 - 465

Received: 28 Mar 2024
Accepted: 28 Nov 2024
Published online: 26 Mar 2025 *

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