SYMMETRY GROUPS AND INTEGRATING FACTORS OF TOTAL DIFFERENTIAL EQUATIONS IN THREE VARIABLES
Keywords:
total differential equation, symmetry group, Lie group, symmetry vector, infinitesimal generator, integrating factor.DOI:
https://doi.org/10.17654/0972096023018Abstract
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.
Received: October 29, 2023
Accepted: December 4, 2023
References
G. W. Bluman and S. C. Anco, Symmetry and integration methods for differential equations, Appl. Math. Sci. 154 (2002), 101-114.
A. R. Forsyth, A Treatise on Differential Equations, 6th ed., Dover, 1996, pp. 309-313.
P. J. Olver, Applications of Lie Groups to Differential Equations, 2nd ed., Springer-Verlag, 1993, pp. 130-137.
P. J. Olver, Applications of Lie Groups to Differential Equations, 2nd ed., Springer-Verlag, 1993, pp. 94-103.
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