Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equation
Nonlinear Studies, The International Journal
We consider the damped externally excited KdV and BBM equations and use an asymptotic perturbation method to analyze the stability of solutions. We consider the primary resonance by defining the detuning parameter. External-excitation and frequency-response curves are shown to exhibit jump and hysteresis phenomena (dis-continuous transitions between two stable solutions) for both KdV and BBM equations.
Usman, Muhammad and Eloe, Paul W., "Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equation" (2012). Mathematics Faculty Publications. 8.