中山大学学报（自然科学版）（中英文）2026，Vol.65Issue(1)：157-168,12.DOI:10.13471/j.cnki.acta.snus.ZR20250163
受扰Calogero-Moser系统的动力学行为:适定性、稳定性和爆破
Dynamics of the perturbed Calogero-Moser system:well-posedness,stability and blow up
摘要
Abstract
We investigate a class of non-integrable two-particle Calogero-Moser systems modulated by a power-law external potential.The local well-posedness of the Cauchy problem is established under the strict initial separation condition for the particles.For suitably prepared initial configurations,local solutions can be extended globally via energy conservation;conversely,negative energy conditions induce(in)finite-time blowup.The linear(in)stability of stationary solutions is analyzed,with their energy serving as a threshold.Numerical investigations employ a fourth-order Runge-Kutta scheme with adaptive step-size control.Simulations demonstrate that the trajectories either converge to steady states or exhibit blowup,depending on the power exponent α and initial conditions.Increasing α accelerates the convergence rate and dampens oscillatory dynamics,promoting a transition from periodic behavior to static equilibrium.关键词
Calogero-Moser系统/适定性/爆破/稳定性Key words
Calogero-Moser system/well-posedness/blow up/stability分类
数理科学引用本文复制引用
刘千乐,王忠,朱伟鹏..受扰Calogero-Moser系统的动力学行为:适定性、稳定性和爆破[J].中山大学学报（自然科学版）（中英文）,2026,65(1):157-168,12.基金项目
Supported by National Natural Science Foundation of China(12201118) （12201118）
Guangdong Basic and Applied Basic Research Foundation(2023A1515010706) （2023A1515010706）
