On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-electro- elastic circular rod

In this study, we improve a new analytical method called the 'Modified exp(-Omega(xi)) expansion function method'. This method is based on the exp(-Omega(xi)) expansion function method. We obtain new analytical solutions expressed by hyperbolic, complex and complex hyperbolic function solutions to the nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod. We plot two- and three-dimensional surfaces of analytical solutions by using Wolfram Mathematica 9.