TY - JOUR

T1 - Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences

AU - Kiessling, Michael K.H.

N1 - Funding Information:
The work reported here has been funded by NSF grant DMS-0807705 . I gratefully acknowledge valuable suggestions by my colleague Shadi Tahvildar-Zadeh. I also thank the two referees for their interesting comments.

PY - 2011/10/31

Y1 - 2011/10/31

N2 - Uniqueness is 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 one 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 exist; any electrostatic (resp. magnetostatic) field is the unique stationary electromagnetic field for the same current-density-free (resp. charge-density-free) sources. These results put to rest some interesting speculations in the physics literature.

AB - Uniqueness is 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 one 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 exist; any electrostatic (resp. magnetostatic) field is the unique stationary electromagnetic field for the same current-density-free (resp. charge-density-free) sources. These results put to rest some interesting speculations in the physics literature.

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U2 - 10.1016/j.physleta.2011.09.052

DO - 10.1016/j.physleta.2011.09.052

M3 - Article

AN - SCOPUS:80054056218

VL - 375

SP - 3925

EP - 3930

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 45

ER -