Work

Integration of a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions

Year: 2024

Type: article

Abstract: UDC 517.9 The method of inverse spectral problem is used to integrate a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions. The evolution of the spectral data for the periodic Dirac operator is introduced in which the coefficient of the Dirac operator is a solution of a nonlinear sine-Gordon–Liouville-type equation. The solvability of the Cauchy problemc is proved for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions. It is shown that the sum of a uniformly convergent functional series constructed by solving the system of Dubrovin differential equations and the first-trace formula satisfies the sine-Gordon–Liouville-type equation.

Source: Ukrains’kyi Matematychnyi Zhurnal

DOI: 10.3842/umzh.v76i8.7610

Authors: A. B. Khasanov, Kh. N. Normurodov, T. G. Khasanov

Institutions: Samarkand State University named after Sharof Rashidov, Urgench State University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4402771936

FWCI:

Cites: 46

Cited by:

Related to: 10