Nonlinear partial differential equations (NPDEs) are of great importance in
applied sciences and engineering including physics, fluid mechanics,
viscoelasticity, diffusion processes, aerodynamics, electrodynamics,
electrostatics, electrochemistry, control theory, mathematical biology, and
so on. The in-depth study study of literature reveals that most of physical
phenomena are nonlinear in nature and hence there is an urgent need to find
appropriate solutions for them. In general, NPDEs are difficult to solve,
especially analytically, therefore, most NPDEs do not have exact analytical
solutions, approximation and numerical methods are widely used. Thus, many
researchers are working on the development of new techniques to obtain the
analytical and numerical solution of NPDEs.

The aim of this work is to develop a simplified analytical method known as
the Laplace Adomian decomposition method (LADM), which is a combination of
two powerful methods: the Laplace transform method and the Adomian
decomposition method to obtain the solution of nonlinear wave-like equation
with variable coefficients in the form