Visualization Study of fKdV Equation Simulation with Matlab.
ABSTRACT Numerical simulation results of fKdV equation are illustrated in the forms of waterfall with Matlab. Matlab can solve many complicated engineering problem and the numerical results can be showed by its excellent graphics. The forced Kortewege-de Vries (fKdV) equation was regarded as a classical nonlinear model when the resonant flow was happened. Which involves a balance between non-linearity and dispersion at leading-order and the effect of the bottom. The pseudo-spectral method based on function approach was good for solving nonlinear equation, and it is convenience to program with the Matlab for PS method. With the results, we can get some conclusion about the effect of the different bottom on surface wave.
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ABSTRACT: The resonant flow of an incompressible, inviscid fluid with surface tension on varying bottoms was researched. The effects of different bottoms on the nonlinear surface waves were analyzed. The waterfall plots of the wave were drawn with Matlab according to the numerical simulation of the fKdV equation with the pseudo-spectral method. From the waterfall plots, the results are obtained as follows: for the convex bottom, the waves system can be viewed as a combination of the effects of forward-step forcing and backwardstep forcing, and these two wave systems respectively radiate upstream and downstream without mutual interaction. Nevertheless, the result for the concave bottom is contrary to the convex one. For some combined bottoms, the wave systems can be considered as the combination of positive forcing and negative forcing.Applied Mathematics and Mechanics 02/2006; 27(3):409-416. · 0.65 Impact Factor
- Journal of Physical Oceanography 10/1978; 8:1016-1024. · 3.18 Impact Factor
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ABSTRACT: Hunter and Scheurle have shown that capillary-gravity water waves in the vicinity of Bond number (Bo)≈ are consistently modelled by the Korteweg-de Vries equation with the addition of a fifth derivative term. This wave equation does not have strict soliton solutions for Bo < because the near-solitons have oscillatory “wings” that extend indefinitely from the core of the wave. However, these solutions are “arbitrarily small perturbations of solitary waves” because the amplitude of the “wings” is exponentially small in the amplitude ϵ of the “core”. Pomeau, Ramani, and Grammaticos have calculated the amplitude of the “wings” by applying matched asymptotics in the complex plane in the limit ϵ → 0.In this article, we describe a mixed Chebyshev/radiation function pseudospectral method which is able to calculate the “weakly non-local solitons” for all ϵ. We show that for fixed phase speed, the solitons form a three-parameter family because the linearized wave equation has three eigensolutions. We also show that one may repeat the soliton with even spacing to create a three-parameter of periodic solutions, which we also compute.Because the amplitude of the “wings” is exponentially small, these non-local capillary gravity solitons are as interesting as the classical, localized solitons that solve the Korteweg-de Vries equation.Physica D Nonlinear Phenomena 01/1991; · 1.67 Impact Factor