In this article, the Laplace decomposition method is implemented to solve nonlinear partial differential equations. Third-order KdV and mKdV equations with initial conditions have been considered to check the validity of the proposed method. Results obtained by this method are compared with the exact solutions in literature numerically as well as graphically and are found to be in good agreement with each other. The proposed method finds the solutions without any discretization, perturbation, linearization, or restrictive assumptions. Obtained results show that the LDM is highly accurate and easy to apply for NLPDEs in various fields.

In the present article substantial Mathematical technique namely LDM and modified LDM has been employed to find the analytical solution of system of NLPDEs. Reliability of these methods were examined by illustrating three examples viz. Drinfield Sokolov (DS) system, coupled Burger's equation and Cauchy problem. Both the methods have many advantages, they converge expeditiously to the exact solution also they do not require linearization, discretization or perturbation. Result obtained by these methods affirms that proposed methods are easy, powerful and efficient technique to find solution of wide class of system on NLPDs.