| A Numerical Study Of An Ill-Posed Boussinesq Equation Arising In Water Waves And Nonlinear Lattices: Filtering And Regularization Techniques (2007) | |||||||||||||
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| . We consider an illposed Boussinesq equation which arises in shallow water waves and nonlinear lattices. This equation has growing and decaying modes in the linear as well as nonlinear regimes and its linearized growth rate oe for short-waves of wavenumber k is given by oe ¸ k 2 . Previous numerical studies have addressed numerical difficulties and construction of approximate solutions for illposed problems with short-wave instability up to oe ¸ k, e.g. Kelvin-Helmholtz (oe ¸ k) and Rayleigh-Taylor (oe ¸ p k) instabilities. These same issues are addressed and critically examined here for the present problem which has more severe short-wave instability. In order to develop numerical techniques for constructing good approximate solutions of this equation, we use a finite difference scheme to investigate the effect of this short-wave instability on the numerical accuracy of the exact solitary wave solution of this equation. Computational evidence is presented which indicates that nume... | |||||||||||||
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