Algebraic method for finding equivalence groups

Abstract

The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the corresponding equivalence algebra. Two versions of the method are presented, where the first involves the automorphism group of this algebra and the second is based on a list of its megaideals. We illustrate the megaideal-based version of the method with the computation of the complete equivalence group of a class of nonlinear wave equations with applications in nonlinear elasticity.

17 pages; revised version; includes results that have been excluded from the journal version of the preprint arXiv:1106.4801v1

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Cited by in corpus (13)

• Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
• Lie symmetries of two-dimensional shallow water equations with variable bottom topography
• Enhanced symmetry analysis of two-dimensional Burgers system
• Extended symmetry analysis of two-dimensional degenerate Burgers equation
• Extended symmetry analysis of isothermal no-slip drift flux model
• Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations
• Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system
• On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis
• Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation
• Lie reductions and exact solutions of dispersionless Nizhnik equation
• Group analysis approach for finding reciprocal transformations for the two-dimensional stationary gasdynamics
• Surprising symmetry properties and exact solutions of Kolmogorov backward equations with power diffusivity
• Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation