On similarity reductions and conservation laws of the two non-linearity terms Benjamin-Bona-Mahoney equation
Keywords:
Benjamin-Bona-Mahoney equation, Lie symmetry group, Scaling symmetry, Optimal system, Homotopy operator, Conservation law.Abstract
In this paper, the Lie group of point symmetries for a
kind of Benjamin-Bona-Mahoney (BBM) equation is obtained by applying the classical Lie symmetry method. An optimal system of sub-algebras of
dimension one for the BBM equation is deduced by classifying the
adjoint representation orbits of the Lie symmetry group.
Then, for any infinitesimal symmetry generators of the Lie group,
the related similarity reductions are generated.
Also, new conservation laws for this equation are constructed by
the method of scaling. The conservation laws densities is calculated by using the concept
of variables weight, scaling symmetry and Euler operator
and their fluxes is computed by applying the homotopy operator.
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