Exact Solution for Nonlinear Wave-Like Equation Using Kharrat-Toma Variational Iteration Method

Abstract

In this study, we present a hybrid methodology for obtaining the exact solution of a specific class of nonlinear partial differential equations, particularly the nonlinear wave-like equation. These equations play a fundamental role in various scientific and engineering disciplines due to their ability to:

-               Model realistic physical phenomena beyond the limitations of idealized linear systems.

-               Describe solitons, which preserve their shape and are widely utilized in fiber optics and fluid dynamics.

-               Enhance the understanding of shock waves, which emerge in fields such as meteorology, astrophysics, and aerodynamics.

-               Serve as a cornerstone in scientific computing, where numerical techniques are employed to solve complex nonlinear problems.

The proposed hybrid scheme combines the semi-analytical Variational Iteration Method (VIM) with the Kharrat-Toma transform, offering a novel and efficient approach for solving nonlinear equations. This integration not only enhances computational efficiency but also provides a robust and straightforward framework for tackling intricate nonlinear systems.