The spectra of the inverse scattering technique (IST) play a crucial role in the physics of nonlinear phenomena. They define the long term evolution of dynamical systems. We present the IST spectral portraits for the extensive three-parameter families of the first order doubly periodic solutions of the nonlinear Schrödinger equation that cover a wide range of physical phenomena such as modulation instability, rogue waves and many other problems with periodic boundary conditions. We relate these spectral portraits with the parameters of the family. We show that there are two qualitatively different types of spectral portraits. A-type spectra consist of two continuous bands: a band of purely imaginary eigenvalues within the interval ##IMG## [http://ej.iop.org/images/1402-4896/95/11/115202/psabbaf3ieqn1.gif] {$[-i,i]$} and a finite band of complex eigenvalues. On the contrary, B-type spectra possess only continuous bands of imaginary eigenvalues all located wi...

中文翻译：

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非线性薛定ding方程的一阶双周期解的IST谱图

逆散射技术（IST）的光谱在非线性现象的物理学中起着至关重要的作用。它们定义了动力系统的长期发展。我们为非线性Schrödinger方程的一阶双周期解的宽泛三参数族提供了IST光谱画像，该问题涵盖了广泛的物理现象，例如调制不稳定性，无赖波和许多其他周期性边界条件的问题。我们将这些光谱肖像与该族的参数相关联。我们表明，光谱肖像在质量上有两种不同的类型。A型谱由两个连续的谱带组成：在区间## IMG ## [http://ej.iop.org/images/1402-4896/95/11/115202/psabbaf3ieqn1.gif ] {$ [-i，i] $}和复杂特征值的有限范围。相反，B型谱仅具有假想特征值的连续带，且所有带都位于...