Results: **2**

#### Two-dimensional supersymmetric quantum mechanics and the **Moutard** **transformations**

... algebra of an extended supersymmetry. We determine the important connection that relates the **Moutard** formula with a problem of «insertion» of a new ground-state eigenvalue to the spectrum of the matrix-valued component of H. And, finally, we discuss the **Moutard** **transformations** and their viability for the higher dimensional cases when d > 2.
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2. Infeld L., Hull T. E. The Factorization Method // Rev. Mod. Phys. Vol. 23. 1951. Р. 21.
3. Beckers ...

#### Algebra method of the construction of the Maxwell equations in a 2D inhomogeneous dielectric

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.
1. Yurova A. A., Yurov A. V., Rudnev M. Darboux ...