Two Different Systematic Techniques to Seek Analytical Solutions of the Higher-Order Modified Boussinesq Equation

Abstract

In this paper, we seek analytical solutions of the higher-order modified Boussinesq equation by two different systematic techniques. Employing the exp $(-\psi (z))$ -expansion method, exact solutions of the mentioned equation, including hyperbolic, exponential, trigonometric, and rational function solutions, have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the higher-order modified Boussinesq equation. It shows that the extended complex method can solve more differential equations in mathematical physics than the complex method. The idea of this paper can be used to the complex nonlinear systems of electrical and electronics engineering.

Keywords

• Higher-order modified Boussinesq equation
• exact solutions
• z))-expansion%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> exp(−ψ(<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">z</italic>))-expansion
• extended complex method