Bilinear form of the regularized long wave equation and its multi-soliton solutions

We consider utmost significant model, namely, the regularized long-wave equation involving dispersion and weedy nonlinearity effects that arises in the nonlinear dynamics of phonon packets in crystals, shallow water, plasma and ion acoustic waves. The Hirota direct approach has been used to deform the model into its bilinear representation. We derive one, two and three solitons solutions from the bilinear form. Moreover, a general formula of N-solitons solution is given of the model. Graphical representations of the achieved solutions are given and found elastic interaction situation of the solitons.