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Mixed Problem for a Nonlinear Schrödinger Equation of Negative Order in the Class of Periodic Infinite-Gap Functions

Kh. N. NormurodovSamarkand State University named after Sharof Rashidov, Samarkand, 140104, UzbekistanА. Б. ХасановSamarkand State University named after Sharof Rashidov, Samarkand, 140104, Uzbekistan

Mathematical Notesjournal2025en

ABI

Annotatsiya

The inverse spectral problem method is applied to integrate a negative-order nonlinear Schrödinger equation in the class of periodic infinite-gap functions. The evolution of spectral data for a periodic Dirac operator whose coefficient is a solution to the negative-order nonlinear Schrödinger equation is introduced. An algorithm for deriving the Dubrovin differential equation system is proposed. The solvability of the Cauchy problem for the infinite Dubrovin differential equation system in the class of twice continuously differentiable periodic infinite-gap functions is proved. It is shown that, for sufficiently smooth initial data, there exists a global solution to the mixed problem for the negative-order nonlinear Schrödinger equation.

Mavzular

Differential Equations and Numerical Methods Differential Equations and Boundary Problems Spectral Theory in Mathematical Physics

Identifikatorlar

DOI: 10.1134/s0001434625602801

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