LIE SYMMETRIES‎, ‎SELF-ADJOINTNESS, AND CONSERVATION LAWS OF THE MONG-AMPERE EQUATION‎

Subject Areas : Mathematical Engineering

Zahra Momennezhad ¹ , Mahdi Najafikhah ²

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Received: 2022-08-25 Accepted : 2022-12-31 Published : 2022-09-01

Keywords: Mong-Ampere equation‎ Lie point symmetry‎ Partial Differential Equations‎ Conservation laws‎, ‎ Conserved vectors,

Abstract :

‎This paper addresses an extended 2-dimensional Mong-Ampere equation By the Lie method‎. The symmetries of Mong-Ampere equation are found ‎and the method of non-linear self-adjointness is applied to the considered equation‎. ‎By applying Ibragimov’s method and Noether operators the infinite set of conservation laws associated with the finite algebra of Lie point symmetry of the Mong-Ampere equation is extracted‎. ‎The corresponding conserved quantities are computed from their respective densities‎.