Proceedings PaperWavelet representation of lower-atmospheric long nonlinear wave dynamics, governed by the Benjamin-Davis-Ono-Burgers equation
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A modified technique is presented for projecting a large class of nonlinear partial differential equations with respect to (x, t) onto a finite number of ordinary differential equations with respect to t. Improved description compared to standard finite-difference or Fourier spectral methods involves using an orthonormal basis of wavelet functions (psi) (nu ,n)(x). Whereas Fourier projection represents the interaction between spatial scales throughout the x- domain, wavelet representation does the same locally. This technique is applied to solving the BDO-Burgers equation, extending previous results for the Burgers equation.