A model of solitary waves in a magnetic-electric-elastic circular rod: analytical and numerical solutions

In this thesis, various solution methods for fourth order EE and MEE nonlinear partial differential equation modeling were discussed. Infinitesimal symmetry generators were found by calculating the elongations of the EE equation by Lie group transformations. With the help of the found infinitesimal symmetry generators , it was made reductions to the ordinary differential equations. Traveling wave solutions were expressed as hyperbolic, trigonometric and rational functions by applying the (G^'/G) method to the same equation. Finally, we obtined to the trigonometric and hyperbolic solutions from Jacobi elliptic function solutions were obtained by applying the F- expansion method to the EE equation. Then based on the trial equation method apply on the MEE equation, the exact solution of a differential equation can be obtained by the process of integration and solutions were obtained by applying tan (φ(ξ)/2) method to the same equation. In addition, some graphical simulations were made using the Maple program to see the behavior of the found solutions.