Group analysis of Benjamin—Bona—Mahony equations with time dependent coefficients

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

Vaneeva, Olena^1 ; Popovych, Roman O.^1,2 ; Sophocleous, Christodoulos^3

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

01601, Ukraine^1

Wolfgang Pauli Institute, Nordbergstraße 15, Wien

A-1090, Austria^2

Department of Mathematics and Statistics, University of Cyprus, Nicosia CY

1678, Cyprus^3

关键词: Benjamin-Bona-mahony equation;    Benjamin-bona-mahony equations;    Equivalence transformations;    Group analysis;    Group classification;    Lie symmetries;    Time-dependent coefficients;    Variable coefficients;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012016/pdf
DOI  :  10.1088/1742-6596/621/1/012016

来源: IOP

【 摘 要 】

Group classification of a class of Benjamin-Bona-Mahony (BBM) equations with time dependent coefficients is carried out. Two equivalent lists of equations possessing Lie symmetry extensions are presented: up to point equivalence within the class of BBM equations and without the simplification by equivalence transformations. It is shown that the complete results can be achieved using either the gauging of arbitrary elements of the class by the equivalence transformations or the method of mapping between classes. As by-product of the second approach the complete group classification of a class of variable-coefficient BBM equations with forcing term is derived.