Melnikov analysis and chaos control of nonlinear dispersive KdV equation under external periodic perturbation

作者：Yin, J. L.^*; Xing, Q. Q.; Tian, L. X.

来源：Indian Journal of Physics and Proceedings of the Indian Association for the Cultivation of Science, 2015, 89(3): 273-279.

DOI：10.1007/s12648-014-0556-9

• Non-smooth solitary waves
• Chaos
• Melnikov's method
• Nonlinear dispersive

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.

• 出版日期2015-3
• 单位江苏大学