外部势中Calogero族模型的出现：对偶、孤子和流体力学
Emergence of Calogero family of models in external potentials: Duality, Solitons and Hydrodynamics
摘要：
我们提出了一个一阶制定的Calogero模型在外部潜力的生成函数，这简化了其对偶形式的推导。在这个公式中，孤立子自然地表现为负质量的粒子。使用这种方法，我们得到的对偶形式的Calogero粒子在外部四次，三角和双曲势，这是已知的可积，但没有已知的对偶公式。我们推导出相应的孤子解决方案，推广早期的结果谐波Calogero系统，并提出了数值结果，证明了孤子运动的可积性。我们还给出了这些模型的集体流体力学公式，并推导出相应的流体孤子解的亚纯领域，评论的稳定性和可积性的问题。
英文摘要：
We present a first-order formulation of the Calogero model in external potentials in terms of a generating function, which simplifies the derivation of its dual form. Solitons naturally appear in this formulation as particles of negative mass. Using this method, we obtain the dual form of Calogero particles in external quartic, trigonometric and hyperbolic potentials, which were known to be integrable but had no known dual formulation. We derive the corresponding soliton solutions, generalizing earlier results for the harmonic Calogero system, and present numerical results that demonstrate the integrable nature of the soliton motion. We also give the collective fluid mechanical formulation of these models and derive the corresponding fluid soliton solutions in terms of meromorphic fields, commenting on issues of stability and integrability.
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