On New Conservation Laws of Fin Equation

Abstract

We study the new conservation forms of the nonlinear fin equation in mathematical physics. In this study, first, Lie point symmetries of the fin equation are identified and classified. Then by using the relationship of Lie symmetry and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math>-symmetry, new<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math>-functions are investigated. In addition, the Jacobi Last Multiplier method and the approach, which is based on the fact<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math>-functions are assumed to be of linear form, are considered as different procedures for lambda symmetry analysis. Finally, the corresponding new conservation laws and invariant solutions of the equation are presented.