Maxwell-Born-Infeld场方程定态解的唯一性结果及其物理意义
Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences
摘要：
在电荷或电流密度为零的条件下，建立了求解无边界空间中非线性Maxwell-Born-Infeld方程的与时间无关的有限能量电磁场的唯一性结果.此外，它还表明，更简单的麦克斯韦-玻恩方程最多承认一个唯一的稳态有限能量电磁场解，没有上述条件。在这些电磁学理论中，出现了以下物理结果：以低于真空光速$c$的速度运动的无源场孤子不存在;任何纯静电场（分别为：静磁场）场是对于相同的无电流密度（分别为无电荷密度）源。我们的结果平息了最近物理学文献中一些有趣的猜测。
英文摘要：
Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density vanishes. In addition, it is also shown that the simpler Maxwell--Born equations admit at most a unique stationary finite-energy electromagnetic field solution, without the above condition. In these theories of electromagnetism, the following physical consequences emerge: source-free field solitons moving at speeds less than the vacuum speed of light $c$ do not exits; any purely electrostatic (resp. magnetostatic) field is the unique stationary electromagnetic field for the same current-density-free (resp. charge-density-free) sources. Our results put to rest some interesting speculations in the recent physics literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
