@article{Khasanov_Normurodov_Khasanov_2024, title={Integration of a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions}, volume={76}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/7610}, DOI={10.3842/umzh.v76i8.7610}, abstractNote={<p>UDC 517.9</p> <p>The method of inverse spectral problem<span class="Apple-converted-space"> </span>is used to integrate a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions.<span class="Apple-converted-space"> </span>The evolution of the spectral data for the periodic Dirac operator<span class="Apple-converted-space"> </span>is introduced in which the coefficient of the Dirac operator is a solution of a nonlinear sine-Gordon–Liouville-type<span class="Apple-converted-space"> </span>equation.<span class="Apple-converted-space"> </span>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.<span class="Apple-converted-space"> </span>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.</p>}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={KhasanovA. B. and NormurodovKh. N. and KhasanovT. G.}, year={2024}, month={Sep.}, pages={1217 - 1234} }