Algebraic method for finding equivalence groups

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Bihlo, Alexander^1,2 ; Cardoso-Bihlo, Elsa Dos Santos^3 ; Popovych, Roman O.^3,4

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's

NL

A1C 5S7, Canada^1

Department of Mathematics, University of British Columbia, Vancouver

BC

V6T 1Z2, Canada^2

Wolfgang Pauli Institut, Universität Wien, Oskar-Morgenstern-Platz 1, Wien

1090, Austria^3

Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivska Str., Kyiv

01601, Ukraine^4

关键词: Algebraic method;    Automorphism groups;    Nonlinear elasticity;    Nonlinear wave equation;    Point symmetry;    System of differential equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012001/pdf
DOI  :  10.1088/1742-6596/621/1/012001

来源: IOP

【 摘 要 】

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.