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.
KeywordsOcean Physics Wave Train Nonlinear Wave Equation Nonlinear Normal Mode Cnoidal Wave
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- M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981.Google Scholar
- A. Degasperis, Nonlinear wave equations solvable by the spectral transform, in Nonlinear Topics in Ocean Physics, ed. by A. R. Osborne, Elsevier, Amsterdam (1989).Google Scholar
- A. R. Osborne, in Soliton Theory: a Survey of Results, ed. by Allan P. Fordy, Manchester University Press (1989).Google Scholar
- A. R. Osborne, in Nonlinear Topics in Ocean Physics, ed. by A. R. Osborne, Elsevier, Amsterdam (1989).Google Scholar
- A. R. Osborne and L. Bergamasco, Physica 18D (1986), 26.Google Scholar
- A. R. Osborne, M. Petti, M. Liberatore and L. Cavaleri, in Computer Modelling in Ocean Engineering, ed. by B. A. Schrefler and O. C. Zienkeiwicz, Balkema, Rotterdam (1988) 99.Google Scholar
- A. R. Osborne and E. Segre, in press Physica D (1990).Google Scholar