TY - JOUR
AU - A. B. Khasanov
AU - Kh. N. Normurodov
AU - T. G. Khasanov
PY - 2024/09/04
Y2 - 2024/10/11
TI - Integration of a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 76
IS - 8
SE - Research articles
DO - 10.3842/umzh.v76i8.7610
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/7610
AB - UDC 517.9The 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.
ER -