Some traveling wave solutions of soliton family

Solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, therelevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modied korteweg-de vries (mkdv) and regularised longwave (rlw) equations usinghomotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initialexpansion coecients using the initial value and boundary conditions. the physical structures of thenonlinear dispersive equation have been investigated for dierent parameters involved. it is shownhow the nature of the waves look like in a simple way by considering the value of a certain singlecombination 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 methodto determine shock or solitary type of solutions, shows its power.