ZHONG Wanxie, WU Feng, SUN Yan, YAO Zheng. Symplectic Water Wave Dynamics[J]. Applied Mathematics and Mechanics, 2018, 39(8): 855-874. doi: 10.21656/1000-0887.390062
Citation: ZHONG Wanxie, WU Feng, SUN Yan, YAO Zheng. Symplectic Water Wave Dynamics[J]. Applied Mathematics and Mechanics, 2018, 39(8): 855-874. doi: 10.21656/1000-0887.390062

Symplectic Water Wave Dynamics

doi: 10.21656/1000-0887.390062
Funds:  The National Natural Science Foundation of China(11472076;51609034;51278298)
  • Received Date: 2018-02-09
  • Rev Recd Date: 2018-04-11
  • Publish Date: 2018-08-15
  • Here, an elementary introduction to the displacement method-based water wave dynamics theory was presented. The periodic travelling wave solutions of the linear water waves and shallow water waves were given. The symplectic perturbation method was proposed to analyze the periodic travelling wave solution for the water system with a general depth. Numerical tests were given to demonstrate the correctness of the proposed method. The present research emphasizes the dynamics property of water waves. By means of the proposed theory, the particle trajectory can be obtained directly, and the periodic travelling wave with sharp surface can be simulated.
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