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

Document Type: Research Articles


Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt.


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