Kink soliton solutions and Hamiltonian dynamics of the fractional generalized Pochhammer-Chree equation via Riccati-Bernoulli sub-ODE method

In this study, we take the fractional Pochhammer-Chree equation with nonlinearity of power-law order m. Using a generalized Riccati-Bernoulli sub-ODE method and a Bäcklund transformation, combined with conformable fractional derivatives, we find the exact solutions of the kink type solitons to this fractional nonlinear model. Qualitative analysis contains 3D plots of integer-order parameter and their respective contour plots, and also 2D profiles of fractional-order parameter (α), to show the impact of fractional dynamics on wave propagation. Moreover, we inspect the dynamical properties of the system in a Hamiltonian setting by examining the phase portraits, time series plot and energy density distributions. The results provide a more in-depth insight into the nonlinear wave patterns feasible in light of the model and emphasize the connection of fractional-order dynamics and solitons. The results add to the theoretical interpretation of higher-order nonlinear wave systems and show that the method of combining analytical techniques with qualitative diagnostics based on Hamiltonian is effective.