Constuction of solitary solutions for nonlinear differential

Here, Adomian decomposition method has been used for nding approximateand numerical solutions of nonlinear dierential dierence equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear dierential dierence equation and Relativistic Toda couplednonlinear dierential-dierence equation are chosen to illustrate the validity andthe great potential of the proposed method. Comparisons are made between theresults of the proposed method and exact solutions. The results show that theAdomian Decomposition Method is an attractive method in solving the non-linear dierential dierence equations. It is worthwhile to mention that theAdomian decomposition method is also easy to be applied to other nonlineardierential dierence equation arising in physics.