Reductions and conservation laws for BBM and modified BBM equations

Khorshidi Maryam; Nadjafikhah Mehdi; Jafari Hossein; Al Qurashi Maysaa

doi:10.1515/math-2016-0101

Open Mathematics (Jan 2016)

Reductions and conservation laws for BBM and modified BBM equations

Khorshidi Maryam,
Nadjafikhah Mehdi,
Jafari Hossein,
Al Qurashi Maysaa

Affiliations

Khorshidi Maryam: Firuzabad Institute of Higher Education, Firuzabad, Fars, Po. Box: 74717-94469, Iran
Nadjafikhah Mehdi: Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 1684613114, Iran
Jafari Hossein: Department of Mathematics, University of Mazandaran, Babolsar, Iran, and Department of Mathematical Sciences, University of South Africa, PO Box 392, UNISA 0003, South Africa
Al Qurashi Maysaa: Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia

DOI: https://doi.org/10.1515/math-2016-0101
Journal volume & issue: Vol. 14, no. 1
pp. 1138 – 1148

Abstract

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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.

Published in Open Mathematics

ISSN: 2391-5455 (Online)
Publisher: De Gruyter
Country of publisher: Poland
LCC subjects: Science: Mathematics
Website: https://www.degruyter.com/journal/key/math/html

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