Melnikov analysis and chaos control of nonlinear dispersive KdV equation under external periodic perturbation
Tóm tắt
The behavior of non-smooth solitary waves switching to chaos is studied. Firstly, we present some singular homoclinic orbits of an unperturbed system. These singular homoclinic orbits correspond to non-smooth solutions. Secondly, we find that the peculiar solitary waves are more likely to be chaos by using the Melnikov theory. Finally, chaos thresholds under different amplitudes and frequencies of a periodic perturbation are given. One interesting finding is that there exists a peculiar perturbation frequency, which has significant effect on the system. The system is not well-controlled under this frequency. However, the system can be well controlled, when the frequency of the perturbation surpasses the peculiar perturbation frequency with fixed parameters of the unperturbed system.
Tài liệu tham khảo
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