Constuction of solitary solutions for nonlinear differential-difference equations via Adomain decomposition method

Abstract

Here, Adomian decomposition method has been used for finding approximate<br />and numerical solutions of nonlinear differential difference equations arising in<br />mathematical physics. Two models of special interest in physics, namely, the<br />Hybrid nonlinear differential difference equation and Relativistic Toda coupled<br />nonlinear differential-difference equation are chosen to illustrate the validity and<br />the great potential of the proposed method. Comparisons are made between the<br />results of the proposed method and exact solutions. The results show that the<br />Adomian Decomposition Method is an attractive method in solving the nonlinear<br />differential difference equations. It is worthwhile to mention that the<br />Adomian decomposition method is also easy to be applied to other nonlinear<br />differential difference equation arising in physics.