Global dynamics near the resonance in the sine-gordon equation

By using the method presented by G. Kovacic and S. Wiggins , the ordinary differential equation (ODE) on the generalized asymptotic inertial manifold(GAIM) of the sine Gordon equation is studied qualitatively. An analytical criterion for existence of orbits homoclinic to the resonance band is given. Under the same parametric values as ones in , by the method in , the existence of pulse orbits connecting to the resonance band is shown, and by comparing with the earlier results, this result explains the chaotic behavior observed in very well.