Numerical Construction of Nonlinear Wave Train Solutions of the Periodic Korteweg-de Vries Equation
We discuss a numerical procedure for the construction of exact, nonlinear wave train solutions of the periodic Korteweg-de Vries (KdV) equation. We use an approach which is effectively a nonlinear Fourier decomposition of the wave motion formulated in terms of the periodic inverse scattering transform µ-representation. We construct solutions which have both narrow and broad-banded Fourier spectra and discuss some physical consequences of the propagation of complex, nonlinear wave motions.
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