Integration of the Negative Order Nonlinear Schrödinger Equation in the Class of Periodic Functions
G. U. UrazboevKhorezm Branch of the Romanovskii Institute of Mathematics, Academy of Sciences of Uzbekistan, 220100, Urgench, UzbekistanМ. М. ХасановUrgench State University, 220100, Urgench, UzbekistanA. K. BabadjanovaKhorezm Branch of the Romanovskii Institute of Mathematics, Academy of Sciences of Uzbekistan, 220100, Urgench, Uzbekistan
ABI
Аннотация
In this paper, we study the negative order nonlinear Schrödinger equation. It is shown that the nonlinear Schrödinger equation of negative order can be integrated by the inverse spectral problem method. The evolution of the spectral data of the Dirac operator with a periodic potential associated with the solution of the negative order nonlinear Schrödinger equation is determined. Obtained results make it possible to apply the inverse problem method to solve the negative order nonlinear Schrödinger equation in the class of periodic functions. Important consequences about the construction algorithm of the solution are provided.
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