Reductions and conservation laws for BBM and modified BBM equations. (English) Zbl 1377.35009
Summary: 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.
MSC:
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
Lie symmetries; group-invariant solutions; optimal system of Lie sub-algebras; adjoint representationReferences:
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