An analysis of the invariance and conservation laws of some classes of
nonlinear Parabolic and Ostrovsky equations and related systems
Abstract
We study various classes of the nonlinear dynamics of some ‘high’ order
parabolic equations (pdes) like the
Benjamin-Bona-Mahony-Peregrine-Burger and the
Oskolkov-Benjamin-Bona-Mahony-Burgers equations that arise in the study
of some wave phenomena. Also, a large class of pdes arising in the
modelling of ocean waves are due to Ostrovsky. We determine the
invariance properties (through the Lie point symmetry generators) of the
nonlinear systems and construct classes of conservation laws for some of
the models above and show how the relationship leads to double
reductions of the systems. This relationship is determined by a recent
result involving ‘multipliers’ that lead to ‘total divergence’.