标题： 隐式孤子在Zabusky-Kruskal实验中的分析：使用周期性反散射变换 显示英文标题

标题： Hidden solitons in the Zabusky-Kruskal experiment: Analysis using the periodic, inverse scattering transform

摘要： 最近对Zabusky--Kruskal实验的数值工作揭示了波形中存在隐藏孤立子。 在这里，使用基于周期性逆散射变换的Osborne非线性傅里叶分析，验证了隐藏孤立子假设，并计算了\emph{精确的}个孤立子的数量、它们的振幅和参考水平。 其他“较少非线性”的振荡模式，虽然不是孤立子，但在色散参数的某些范围内也被发现具有非平凡的能量贡献。 此外，发现参考水平是色散参数的非单调函数。 最后，在大色散的情况下，我们证明了一项非线性傅里叶级数在雅可比椭圆函数方面能给出非常精确的近似解。 显示英文摘要

摘要： 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 \emph{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.