Classification of Jacobi solutions of double dispersion equation in uniform and inhomogeneous Murnaghan's rod

The double dispersion equation comprising the Lame coefficient, nonlinear coefficient, and Poisson ratio components is described as the uniform and inhomogeneous Murnaghan's rod by A. M. Samsonov in Samsonov (2001). In this work, we apply the F expansion method to the double dispersion equation in the uniform and inhomogeneous Murnaghan's rod, extract the Jacobi elliptic function solution, and classify it into six families of unique solutions. The necessary condition and the degeneration of the Jacobi solutions based upon the elliptic function modulus are given for each solution. The six classifications are formed based on the solutions of the algebraic equations.