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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.