No abstract

In this work, authors propose some modifications Adomian decomposition method to get some accurate closed form approximate or exact solutions of Duffing- and Li´enard-type nonlinear ordinary differential equations.Results obtained by the revised scheme have been exploited subsequently to derive constraints among parameters to get the solutions to be bounded. The present scheme appears to be efficient and may be regarded as the confluence of apparently different methods for getting exact solutions for a variety of nonlinear ordinary differential equations appearing as mathematical models in several physical processes.

No abstract

No abstract

In this work, the rapidly convergent approximation method (RCAM) followed by appropriate modifications is applied to obtain piecewise smooth solutions and conserved quantities of a Liénard‐type equation and some important nonlinear partial differential equations reducible to former one. Explicit parameter dependence of the solution has been sensibly used to determine parameter dependence of the constant of the motion as well as the domain in the parameter space for which the piecewise smooth solution is bounded. Solution of Liénard‐type equation is then used to find piecewise smooth traveling wave solutions and corresponding conserved quantities of nonlinear Schrödinger equation. These findings affirm the efficiency of the RCAM for analytical exercise of variety of nonlinear systems of ordinary/partial differential equations appear as mathematical model of physical processes.