Integration of a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions
Анотація
УДК 517.9
Інтегрування нелінійного рівняння типу синус-Гордона-Ліувілля у класі періодичних нескінченнозонних функцій
Метод оберненої спектральної задачі використовується для інтегрування нелінійного рівняння типу синус-Гордона–Ліувілля у класі періодичних нескінченнозонних функцій. Розглянуто еволюцію спектральних даних періодичного оператора Дірака, коефіцієнт якого є розв’язком нелінійного рівняння типу синус-Гордона–Ліувілля. Доведено розв’язність задачі Коші для нескінченної системи диференціальних рівнянь Дубровіна у класі тричі неперервно диференційовних періодичних нескінченнозонних функцій. Показано, що сума рівномірно збіжного функціонального ряду, побудованого в результаті розв’язування системи диференціальних рівнянь Дубровіна та першої формули сліду, задовольняє рівняння типу синус-Гордона–Ліувілля.
Посилання
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