On exact solutions of magneto-electro-elastic rods equation

Abstract

Magneto-electro-elastic materials represent a new class of materials with various potential applications in nanotechnology and it is of great importance due to its forward-looking energy conversion properties. In this study, we investigated the 4th order nonlinear evolution equation modeling solitary waves in a magneto-electro-elastic circular rod. We have constructed the exact solutions of the considered model with a new extended direct algebraic scheme. The solutions obtained by using this technique contain various new solution families in addition to the solutions obtained by the other integration architectures. Numerical simulations of the obtained solutions for different values of the parameters were also performed. In addition, we transformed the one of the exact solutions found by the new extended direct algebra method into the new solution under the symmetry transformation. Finally, we apply the stability property via the properties of the Hamilton system to the some retrieved solutions.