Maqola

Cauchy Problem for the Nonlinear Liouville Equation in the Class of Periodic Infinite-Gap Functions

А. Б. ХасановSamarkand State University, Samarkand, 140104, UzbekistanKh. N. NormurodovSamarkand State University, Samarkand, 140104, UzbekistanU. O. KhudayorovSamarkand State Institute of Architecture and Construction, Samarkand, 140143, Uzbekistan

Differential Equationsjournal2023en

ABI

Annotatsiya

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

Mavzular

Differential Equations and Numerical Methods Nonlinear Waves and Solitons Differential Equations and Boundary Problems

Identifikatorlar

DOI: 10.1134/s00122661230100087

Iqtiboslar va manbalar

6 ta iqtibos 18 ta foydalanilgan manba

Koʻrsatkichlar — AkademScholar · Tez orada