On the conservation laws and traveling wave solutions to the bbm equation

Abstract

In this study the Benjamin-Bona-Mahony (BBM) equation, modelling long wave motion in nonlinear dispersive systems is discussed. Applying the new general theorem on nonlocal conservation laws [1], (N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., Vol. 333 (2007), pp. 311-328) and using the symmetries of the model equation conservation laws are discussed. Also, we construct reductions and solutions of the BBM equation using inverse variational and symmetry methods.