Soliton solutions of a Calogero model in a harmonic potential
Soliton solutions of a Calogero model in a harmonic potential
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谐波势中 Calogero 模型的孤子解
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Kulkarni
中科院分区：
文献类型：
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作者：
A. Abanov;A. Gromov;M. Kulkarni
已知外调和势中的经典Calogero模型对任意数量的粒子都是可积的。在这里，我们认为减少发挥作用的“孤子”解决方案的模型。我们得到这些解决方案的模型与有限数量的粒子和流体动力学限制。在后者的限制，该模型是由流体动力学方程的连续密度和速度场。在这种情况下，孤子解是流体动力学模型的有限维简化，描述了非平凡背景中密度和速度块的传播。
A classical Calogero model in an external harmonic potential is known to be integrable for any number of particles. We consider here reductions which play a role of the ‘soliton’ solutions of the model. We obtain these solutions both for the model with finite number of particles and in a hydrodynamic limit. In the latter limit, the model is described by hydrodynamic equations on continuous density and velocity fields. Soliton solutions in this case are finite-dimensional reductions of the hydrodynamic model and describe the propagation of lumps of density and velocity in the nontrivial background.