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Bounded traveling waves of the oceanic currents motion equations |
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| Authors: | Qian Liu Yuqian Zhou Shouming Zhong |
| Institution: | a School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China b School of Computer Science and Technology, Southwest University for Nationalities, Chengdu, Sichuan 610041, PR China c School of Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, PR China d School of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China |
| Abstract: | The bifurcation methods of differential equations are employed to investigate traveling waves of the oceanic currents motion equations. The sufficient conditions to guarantee the existence of different kinds of bounded traveling wave solutions are rigorously determined. Further, due to the existence of a singular line in the corresponding traveling wave system, the smooth periodic traveling wave solutions gradually lose their smoothness and evolve to periodic cusp waves. The results of numerical simulation accord with theoretical analysis. |
| Keywords: | Bifurcation Oceanic currents motion equations Solitary waves Cusp waves Periodic traveling waves |
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