Weakly Nonlinear Waves Propagating in Hyperelastic Cylindrical Rod Tranquility of Compressible Murnaghan Material

The compressible Murnaghan’s materials composed in the hyperelastic rod describing the far-field equation as the KdV equation for the weak nonliear waves traversing inside the rod is studied with the F expansion method and solved to get the exact elliptic function solutions. The necessary condition for the each Jacobi solutions are reported. The 2D and 3D graphicals are simulated for certain periodic waves. The necessary condition of selection of material and geometric constants for distraction free wave travelling are suggested.