Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer-Chree equation

In this article, propagation of solitary wave solutions to the Pochhammer-Chree equation(PC) are investigated. Different kinds of solutions like bright-dark, kink, singular, hyperbolic, rational, trigonometric as well as Jacobi elliptic function solutions are obtained. The innovative methodology used to extract the solitary wave is known as Φ⁶-model expansion method. Moreover, the modulation instability (MI) analysis of governing equation is also discussed. Against the appropriate choices of parameters, two and three dimensional and contour graphs are also sketched. The obtained outcomes are more general and fresh and show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations. (paper)