Abstract A second order non-perturbative trapping scenario is employed to show the existence of a new Gaussian type of solitary electron holes. Use is thereby made of Schamel's pseudo-potential method, the only method that can guarantee the completeness of an equilibrium solution of the Vlasov-Poisson system in addition to its existence. The new potential is of the form e − X ( x ) 2 where X ( x ) = s i n h ( x ) and is hence reminiscent of the Gaussian potential appearing in its “second generation”. The simultaneous presence of both trapping generations hence establishes a one-parametric continuum spectrum of solitary electron holes all of them being, through appropriate fitting, potential candidates for identifying structures in experimental observations and numerical simulations. Taking into account the possibility of many more trapping scenarios moreover, a unique identification of structures, the desired goal expressed in the current literature when interpreting structure formation, is therefore not achievable. Origin of this intrinsic ambiguity is the loss of mathematical stringency in the kinetic regime through chaos triggered by the ergodic particle trajectories in the resonant region of phase space in the single particle – coherent wave interaction process.

中文翻译：

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由于二阶、非微扰电子俘获和实验中空穴结构可识别性的一般损失，高斯型新电子空穴

摘要 采用二阶非微扰俘获场景来证明一种新的高斯型孤立电子空穴的存在。因此使用了 Schamel 的赝势方法，这是除了 Vlasov-Poisson 系统的存在性之外还能保证其平衡解的完整性的唯一方法。新势的形式为 e − X ( x ) 2 ，其中 X ( x ) = sinh ( x )，因此让人想起出现在“第二代”中的高斯势。因此，两个捕获代的同时存在建立了孤立电子空穴的单参数连续谱，通过适当的拟合，所有这些都是在实验观察和数值模拟中识别结构的潜在候选者。此外，考虑到更多诱捕场景的可能性，因此无法实现结构的独特识别，即当前文献中在解释结构形成时所表达的预期目标。这种内在模糊性的起源是由于在单粒子-相干波相互作用过程中相空间共振区域中的遍历粒子轨迹引发的混沌而导致动力学体系中数学严格性的丧失。