Article

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

Lobachevskii Journal of Mathematicsjournal2024en

ABI

Abstract

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.

Topics

Numerical methods for differential equations Nonlinear Waves and Solitons Fractional Differential Equations Solutions

Identifiers

DOI: 10.1134/s1995080224606106

Citations and references

Cited by 2 30 references

Metrics — AkademScholar · Coming soon