Algebra method of the construction of the Maxwell equations in a 2D inhomogeneous dielectric
- Pages
- 34-37
Abstract
We study discrete isospectral symmetries for the linear problem in spatial dimensions two, by developing a Darboux (Moutard) transformation formalism for this problem. As an application, we construct some singular and nonsingular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.
Reference
1. Yurova A. A., Yurov A. V., Rudnev M. Darboux transformation for classical acoustic spectral problem // Interntional Journal of Mathematics and Mathematical Sciences. 2003. № 49. P. 3123—3142.
2. Moutard Th. Sur la construction des equations de la forme 1 d2z (x, y) z dxdy, qui admettent une integrale generale explicite // J. Ecole Polytechnique. 1878. № 45. P. 1—11.
3. Matveev V. B., Salle M. A. Darboux Transformation and Solitons. B.; Heidelberg, 1991.
4. Darboux G. Lecons sur la theorie generale des surfaces et les applications geometriques du calcul infinitesimal. P., 1915. Vol. 2.
5. Crum M. M. Associated Sturm-Liouville systems // Quart. J. Math. 1955. Ser. 2, vol. 6. P. 121—127.
6. Veselov A. P., Shabat A. B. Dressing Chains and Spectral Theory of the Schrödinger Operator // Funkts. Anal. Prilozh. 1993. Vol. 27, Issue 2. P. 1—2.1.