Some traveling wave solutions of soliton family

Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modied Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion coecients using the initial value and boundary conditions. The physical structures of the nonlinear dispersive equation have been investigated for different parameters involved. It is shown how the nature of the waves look like in a simple way by considering the value of a certain single combination of constant parameters. The proposed scheme is standard, direct and computerized, which allow us to do complicated and tedious algebraic calculations. The ease of using this method to determine shock or solitary type of solutions, shows its power.

Keywords:

Nonlinear partial differential equations , solitary waves , Homotopy perturbation method (HPM)