Journal of Computational Physics
Automatic algorithm for the numerical inverse scattering transform of the Korteweg-de Vries equation
Mathematics and Computers in Simulation - Special issue: solitons, nonlinear wave equations and computation
Visiometrics and modeling in computational fluid dynamics
Mathematics and Computers in Simulation - Special issue on nonlinear dynamic phenomena in physical, chemical and biological systems
On the long-time behaviour of soliton ensembles
Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
Journal of Computational Physics
Propagation of sech2-type solitary waves in hierarchical KdV-type systems
Mathematics and Computers in Simulation
Internal solitary waves in the ocean: Analysis using the periodic, inverse scattering transform
Mathematics and Computers in Simulation
On solitons in microstructured solids and granular materials
Mathematics and Computers in Simulation
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Recent numerical work on the Zabusky-Kruskal experiment has revealed, amongst other things, the existence of hidden solitons in the wave profile. Here, using Osborne's nonlinear Fourier analysis, which is based on the periodic, inverse scattering transform, the hidden soliton hypothesis is corroborated, and the exact number of solitons, their amplitudes and their reference level is computed. Other ''less nonlinear'' oscillation modes, which are not solitons, are also found to have nontrivial energy contributions over certain ranges of the dispersion parameter. In addition, the reference level is found to be a non-monotone function of the dispersion parameter. Finally, in the case of large dispersion, we show that the one-term nonlinear Fourier series yields a very accurate approximate solution in terms of Jacobian elliptic functions.