C. J. Papachristou
Published 2015-05-26Version 1
B\"acklund transformations (BTs) are a useful tool for integrating partial differential equations (PDEs), especially nonlinear ones. However, their significance in linear problems should not be underestimated. In fact, an important linear system of PDEs in Physics, namely, the Maxwell equations of Electromagnetism, constitutes a BT, as explained in this article. This BT relates solutions of the wave equations for the electric and the magnetic field.
Comments: 13 pages. arXiv admin note: text overlap with arXiv:0803.3688
Classical and Quantum Electrodynamics Concept Based on Maxwell Equations' Symmetry
The Construction of the mKdV $N$-soliton Solution by the Bäcklund Transformation
The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, and Maxwell Equations
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