Analytical solutions of the Caudrey-Dodd-Gibbon equation using Khater II and variational iteration methods.

This study focuses on solving the Caudrey-Dodd-Gibbon ( ) equation using the Khater II ( ) method and the Variational Iteration ( ) method. The equation is a pivotal mathematical model in nonlinear wave dynamics, essential for understanding the evolution, interaction, and preservation of wave forms in dispersive media. Its applications span various fields, including fluid dynamics, nonlinear optics, and plasma physics, where it plays a crucial role in analyzing solitons and complex wave interactions.

High accuracy solutions for the Pochhammer-Chree equation in elastic media.

This study investigates the nonlinear Pochhammer-Chree equation, a model crucial for understanding wave propagation in elastic rods, through the application of the Khater III method. The research aims to derive precise analytical solutions and validate them using He's variational iteration method (VIM). The Pochhammer-Chree equation's relationship to other nonlinear evolution equations, such as the Korteweg-de Vries and nonlinear Schrödinger equations, underscores its significance in the field of nonlinear wave dynamics.