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G. A. El, R. H. Grimshaw and A. M. Kamchatnov, “Evolution of Solitary Waves and Undular Bores in ShallowWater Ows over a Gradual Slope with Bottom Friction,” Journal of Fluid Mechanics, Vol. 585, 2007, pp. 213-244. doi:10.1017/S0022112007006817

has been cited by the following article:

• TITLE: Numerical Simulation of Nonlinear Surface Gravity Waves Transformation under Shallow-Water Conditions

  AUTHORS: Iftikhar B. Abbasov

  KEYWORDS: Equations of Shallow-Water; Numerical Modelling; Nonlinear Surface Gravity Waves; Transformation of Surface Wave Profile

  JOURNAL NAME: Applied Mathematics, Vol.3 No.2, February 23, 2012

  ABSTRACT: This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions. The discrete model is built from non-linear shallow-water equations. Are resulted boundary and initial conditions. The method of splitting into physical processes receives system from three equations. Then we define the approximation order and investigate stability conditions of the discrete model. The sweep method was used to calculate the system of equations. This work presents surface gravity wave profiles for different propagation phases.