In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.
@article{bwmeta1.element.doi-10_1515_math-2016-0101,
author = {Maryam Khorshidi and Mehdi Nadjafikhah and Hossein Jafari and Maysaa Al Qurashi},
title = {Reductions and conservation laws for BBM and modified BBM equations},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {1138-1148},
zbl = {06675365},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0101}
}
Maryam Khorshidi; Mehdi Nadjafikhah; Hossein Jafari; Maysaa Al Qurashi. Reductions and conservation laws for BBM and modified BBM equations. Open Mathematics, Tome 14 (2016) pp. 1138-1148. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0101/