Study of Two Sinusoidal Forcing Terms in a Geo-KdV Model

In this study, a Geo-KdV model is considered which is typically an extended KdV Equation with an extra term responsible for the Coriolis effect on wave dynamics, with the Coriolis parameter denoted by [Formula: see text]. While most of the studies available in the literature treat [Formula: see text] as constant, in this study, the model is investigated for its stability for a range of values of [Formula: see text] by employing certain standard tools from bifurcation analysis such as phase portraits, bifurcation maps and the Lyapunov exponents. Based on the analysis, it is found that the model can exhibit chaotic behavior for certain critical values of [Formula: see text]. Furthermore, motivated by studies in plasma physics, seismology and other related areas available in the literature, two distinct forcing terms, namely, [Formula: see text] and [Formula: see text] are considered as perturbations in the model. Here, [Formula: see text] and [Formula: see text] denote the forcing and the frequency parameters, respectively. Also, t is time and u is the free surface elevation included in the model equation. It’s important to note that while the forcing terms may seem similar, they have different effects on the model problem; [Formula: see text] results in a two-dimensional system, while [Formula: see text] leads to a three-dimensional system. A comparative study of these forcing terms is done for certain critical values of these parameters using the standard theory of dynamical systems. It is found that the system exhibits aperiodic, quasi-periodic and chaos-like behaviors for these critical values of the parameters. Confirmation of chaos-like behavior under various conditions in the Geo-KdV model is established by employing bifurcation analysis tools.