Regularized integrals of motion for the Korteweg – de-Vries equation in the class of nondecreasing functions

• Дата: 2015
• Автори: Andreev, K. N., Khruslov, E. Ya., Андреев, К. Н., Хруслов, Е. Я.
• Формат: Стаття
• Мова: Російська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2015
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/2093
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We study the Cauchy problem for the Korteweg–de-Vries equation in the class of functions approaching a finite- zone periodic solution of the KdV equation as $x → −∞$ and 0 as $x → +∞$. We prove the existence of infinitely many “regularized” integrals of motion for the solutions $u(x, t)$ of the Cauc...