constuction of solitary solutions for nonlinear differential-difference equations via adomain decomposition method

here, adomian decomposition method has been used for finding approximateand numerical solutions of nonlinear differential difference equations arising inmathematical physics. two models of special interest in physics, namely, thehybrid nonlinear differential difference equation and relativistic toda couplednonlinear differential-difference 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 nonlineardifferential difference equations. it is worthwhile to mention that theadomian decomposition method is also easy to be applied to other nonlineardifferential difference equation arising in physics.