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Yi-feng ZHANG, Rui-jie LI. 2012: Numerical solutions for two nonlinear wave equations. Water Science and Engineering, 5(4): 410-418. doi: 10.3882/j.issn.1674-2370.2012.04.005
Citation: Yi-feng ZHANG, Rui-jie LI. 2012: Numerical solutions for two nonlinear wave equations. Water Science and Engineering, 5(4): 410-418. doi: 10.3882/j.issn.1674-2370.2012.04.005
shu

Numerical solutions for two nonlinear wave equations

doi: 10.3882/j.issn.1674-2370.2012.04.005
  • 1.

    School of Civil Engineering, Tianjin University, Tianjin 300072, P. R. China

  • 2.

    Tianjin Research Institute for Water Transport Engineering of Ministry of Transport, Tianjin 300456, P. R. China

  • 3.

    Key Laboratory of Coastal Disaster and Defence of Ministry of Education, Hohai University, Nanjing 210098, P. R. China

Funds:  This work was supported by the Central Public-Interest Scientific Institution Basal Research Fund of China (Grant No. TKS100108).
More Information
  • Corresponding author: Yi-feng ZHANG
  • Received Date: 2010-10-20
  • Rev Recd Date: 2012-09-06
    Abstract
  • The split-step pseudo-spectral method is a useful method for solving nonlinear wave equations. However, it is not widely used because of the limitation of the periodic boundary condition. In this paper, the method is modified at its second step by avoiding transforming the wave height function into a frequency domain function. Thus, the periodic boundary condition is not required, and the new method is easy to implement. In order to validate its performance, the proposed method was used to solve the nonlinear parabolic mild-slope equation and the spatial modified nonlinear Schrödinger (MNLS) equation, which were used to model the wave propagation under different bathymetric conditions. Good agreement between the numerical and experimental results shows that the present method is effective and efficient in solving nonlinear wave equations.

     

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