We study the Calogero–Moser derivative nonlinear Schrödinger NLS equation posed on the Hardy–Sobolev space with suitable . By using a Lax pair structure for this ‐critical equation, we prove global well‐posedness for and initial data with sub‐critical or critical ‐mass . Moreover, we prove uniqueness of ground states and also classify all traveling solitary waves. Finally, we study in detail the class of multi‐soliton solutions and we prove that they exhibit energy cascades in the following strong sense such that as for every .

中文翻译：

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Calogero–Moser 导数非线性薛定谔方程

我们研究 Calogero–Moser 导数非线性薛定谔 NLS 方程在 Hardy-Sobolev 空间上提出，具有合适的 .通过对这个临界方程使用 Lax 对结构，我们证明了具有亚临界或临界质量的初始数据的全局适定性。此外，我们证明了基态的唯一性，并对所有行进的孤立波进行了分类。最后，我们详细研究了多孤子解的类别，并证明它们在以下强意义上表现出能量级联，例如对于每个 。