麦克斯韦场中质心固定的旋转电荷的孤子稳定性及其吸引性研究
On stability of solitons and their attraction for a rotating charge with fixed mass center in the Maxwell field
AI总结：
本文研究麦克斯韦场中质心固定旋转电荷的孤子解，利用能量守恒定律证明其李雅普诺夫稳定性和轨道稳定性，并通过角动量论证排除有限角动量孤子的吸引现象。
摘要：
我们考虑麦克斯韦方程组与洛伦兹力矩方程构成的系统，该系统描述电荷在电磁场中的运动。在电荷分布和初始场满足一定对称性条件下，电荷的质心保持固定，电荷绕质心旋转。该系统存在稳态孤子型解。我们利用能量守恒定律研究孤子的李雅普诺夫稳定性和轨道稳定性。我们还通过角动量论证表明，在具有相同角动量的状态曲面上，不存在向有限角动量孤子的吸引。参考文献：23篇。
英文摘要：
We consider the system of Maxwell equations and Lorentz torque equation which describes a motion of charge in electromagnetic field. Under certain symmetry conditions on charge distribution and on initial fields the mass center of the charge remains fixed and the charge rotates around it. The system admits stationary soliton-type solutions. We study the Lyapunov and the orbital stability of the solitons exploiting the energy conservation law. We also show, by the angular momentum argument, that there is no attraction to a soliton of finite angular momentum on the surface of states of the same angular momentum. The bibliography: 23 refs.
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