Abstract
The modified regularized long wave (MRLW) equation is solved numerically by Adomian decomposition method (ADM) with some initial conditions. The method leads to high accurate and efficient results. Three polynomial invariant conditions are evaluated to determine the conservation properties of the problem. The convergence of Adomian decomposition method applied to the MRLW equation is proved. Moreover, the interaction of solitons and the development of the Maxwellian initial condition into solitary waves are considered.