Subharmonic bifurcations and chaos for the traveling wave solutions of the compound Kdv–Burgers equation with external and parametrical excitations

The subharmonic bifurcations and chaotic motions are investigated both analytically and numerically for the traveling solutions of compound Kdv–Burgers equation with external and parametrical excitations. The critical curves separating the chaotic and non-chaotic regions are obtained. The chaotic feature on the system parameters are discussed in detail. Some new dynamical phenomena including the “controllable frequency” are presented. The conditions for subharmonic bifurcations are also obtained. Numerical results are given, which verify the analytical ones.