Global Existence and Uniqueness of Periodic Waves for a Perturbed Combined Double-Dispersive Equation

In this paper,we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation(PDE).The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation(ODE).The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle,which corresponds the periodic traveling wave for the PDE model.The main tool is the Abelian integral taken from Poincaré bifurcation theory.Simulation is carried out to verify the theoretical result.