<p>The thermodynamic soliton model of action potential has been established as a credible alternative for studying the dynamics of nerve impulse propagation in contrast to the Hodgkin-Huxley model, which explains the nerve impulse as a result of ion exchanges across the neuronal membrane. Thermodynamic soliton model views the impulse as a soliton linked to thermodynamic processes that accompany the generation of an action potential. In this work, we investigate an extended thermodynamic soliton model of action potential by considering a generalized Boussinesq equation with third and fourth order nonlinearities. By applying reductive perturbation and multiple scale expansion, we derive the variable coefficient nonlinear Schrödinger equation governing the envelope dynamics. Using Hirota bilinear method, we construct exact analytic one- and two- soliton solutions revealing distinct configurations including bell, breather-like and kink soliton solutions. We also demonstrate the simultaneous pulse splitting of two solitons, resulting in the formation of soliton doublets that show a dynamical behavior qualitatively similar to certain neuronal firing patterns. The parameter dependent interaction of two solitons is analysed, revealing energy redistribution and amplitude flipping mechanisms influenced by system parameters. Also, we perform the linear stability analysis and demonstrate that the eigenvalue spectra shows the quartet symmetry similar to conservative and parity-time symmetric systems which is identified as a pseudo-Hamiltonian Hopf bifurcation. Furthermore, numerical simulations are performed and found to be in agreement with the analytical solution, along with the emergence of a hyperpolarization phase. Additionally, we systematically derive the families of solutions using the extended F-expansion method. These results provide novel insights into nonlinear mechanisms underlying action potential propagation based on soliton theory.</p>