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The present exploration studies the dynamical profile, multistability and soliton solution of ion-acoustic waves (IAWs) in plasma physics. The new auxiliary equation approach is implemented to compute a wide range of solitary wave structures of different types. The dynamical profile is studied by using the bifurcation theory. This system is converted into a planar dynamical system via the Galilean transformation. Taking different cases of its coefficients, the phase plane analysis of this resultant dynamical system is performed. The phase diagrams show the different characteristics of the equilibrium points of the planar dynamical system. The quasi-periodic behaviors, multistability of this planar dynamical system are done by adding the perturbation term. The sensitivity assessment of this perturbed dynamical system is performed by taking different initial constraints.
Fatima et al. (Sun,) studied this question.