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This article is cited in 8 scientific papers (total in 8 papers)
Research Papers
The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions
G. A. Mannonov, A. B. Khasanov Samarkand State University
Abstract:
The method of inverse spectral problem is used to integrate the nonlinear Hirota equation in the class of periodic infinite-zone functions. The evolution of spectral data is introduced for the periodic Dirac operator whose coefficient is the solution of the nonlinear Hirota equation. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of five times continuously differentiable periodic infinite-zone functions is shown. In addition, it is proved that if the initial function is real-analytic and $\pi$-periodic, then the solution of the Cauchy problem for the Hirota equation is also a real-analytic function of the variable $x$; next, if the number $\pi/2$ is a period (antiperiod) of the initial function, then the number $\pi/2$ is a period (antiperiod) in the variable $x$ for the solution of the Cauchy problem for the Hirota equation.
Keywords:
Hirota equation, Dirac operator, Spectral data, Dubrovin system, trace formulas.
Received: 15.02.2022
Citation:
G. A. Mannonov, A. B. Khasanov, “The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions”, Algebra i Analiz, 34:5 (2022), 139–172; St. Petersburg Math. J., 34:5 (2023), 821–845
Linking options:
https://www.mathnet.ru/eng/aa1833 https://www.mathnet.ru/eng/aa/v34/i5/p139
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Abstract page: | 166 | Full-text PDF : | 11 | References: | 32 | First page: | 15 |
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