Lax representation and bi-Hamiltonian structure of nonlinear Qiao model

This paper explores accurate, stable, and novel soliton wave solutions of the nonlinear Qiao model. This model, which was derived in 2007, possesses a Lax representation and bi-Hamiltonian structure, where it is a second positive member in the utterly integrable hierarchy. The well-known generalized extended tanh-function method is employed to construct novel soliton wave solutions. The stable property of the obtained solutions is examined along with the Hamiltonian system’s characterizations. Furthermore, the accuracy of the obtained solutions is checked by comparing it with the model’s semi-analytical solutions that have been obtained by employing the variational iteration (VI) method. The obtained analytical and semi-analytical solutions are demonstrated through some distinct graphs to show more physical and dynamical behavior of the investigated model. The used analytical and semi-analytical schemes’ performance is checked to show if it is effective and powerful.