| Abstract: |
| Nonlinear dispersive equations are omnipresent in applications in hydrodynamics, nonlinear optics, plasma physics,... but their mathematical description is challenging since they can have stable solitary waves, but also zones of rapid modulated oscillations called dispersive shock waves and even a blow-up, a loss of regularity in finite time. For the numerical description spectral methods are the preferred choice since they minimise the introduction of numerical dissipation which could suppress the dispersive effects to be studied. For smooth rapidly decreasing or periodic functions, FFT techniques are preferred. But we will also discuss spectral methods, for instance Chebyshev polynomials, for slowly decaying or piecewise smooth functions. Several examples are discussed, also for fractional derivatives. |
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