arXiv subjects
Publications and source records attributed to Leonid Nizhnik.
The Hamiltonian form of the (2+1) nonlinear integrable Schrödinger equation and the system of two (2+1) nonlinear analogue of the mKdV equation is proved. A well--posed Cauchy problem is formulated and the solvability of such a problem for the (2+1) nonlinear analogue of the mKdV equation is proved.
We give an abstract definition of a one-dimensional Schrödinger operator with $δ'$-interaction on an arbitrary set~$Γ$ of Lebesgue measure zero. The number of negative eigenvalues of such an operator is at least as large as the number of those isolated points of the set~$Γ$ that have negative values of the intensity constants of the $δ'$-interaction. In the case where the set~$Γ$ is endowed with a Radon measure, we give constructive examples of such operators having an infinite number of negative eigenvalues.