In this paper, we define the symmetry group of a total differential equation in three variables, give the infinitesimal criterion for invariance under the action of a Lie group, and provide a formula for an integrating factor in terms of the symmetry vector.

total differential equation, symmetry group, Lie group, symmetry vector, infinitesimal generator, integrating factor.

Received: October 29, 2023;  Accepted: December 4, 2023; Published: December 13, 2023

How to cite this article: Sam Melkonian, Symmetry groups and integrating factors of total differential equations in three variables, Far East Journal of Applied Mathematics 116(4) (2023), 377-391. http://dx.doi.org/10.17654/0972096023018

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] G. W. Bluman and S. C. Anco, Symmetry and integration methods for differential equations, Appl. Math. Sci. 154 (2002), 101-114.
[2] A. R. Forsyth, A Treatise on Differential Equations, 6th ed., Dover, 1996, pp. 309-313.
[3] P. J. Olver, Applications of Lie Groups to Differential Equations, 2nd ed., Springer-Verlag, 1993, pp. 130-137.
[4] P. J. Olver, Applications of Lie Groups to Differential Equations, 2nd ed., Springer-Verlag, 1993, pp. 94-103.