On Steady-State Multiple Resonances for a Modified Bretherton Equation

In this article, a modified Bretherton equation is considered to further check if steady-state multiple resonances exist not only for water waves but also for other dispersive medium. The linear resonance condition analysis shows that different components may interact with each other so multiple resonances may happen. Convergent steady-state solutions are obtained by solution procedure based on the homotopy analysis method (HAM) and the collocation method. Amplitude spectrum analysis confirms that more components indeed join the resonance as the nonlinearity increases. This article suggests that steady-state multiple resonance may exist in other dispersive system.