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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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 ...