Understanding soliton propagation and stability in nonlinear media with multistable states

This manuscript examines the nonlinear wave propagation problem, which can be described by the Estevez-Mansfield-Clarkson equation, which has applications in nonlinear dispersive media, optical systems, plasma physics, and fluid dynamics. The originality of this manuscript lies in the construction of various kinds of traveling wave solutions of the Estevez-Mansfield-Clarkson equation by employing the generalized Riccati equation mapping method and the modified extended tanh method, which can be used to obtain various kinds of bright, dark, singular, and periodic solitons. Moreover, numerical visualizations of the solutions are performed to examine the solutions’ robustness with respect to various parameters, and the multistability of the nonlinear wave systems is also examined by employing the phase space method, which shows that multiple stable states exist, indicating that the nonlinear wave systems are highly sensitive to the initial states.