TY - JOUR AU - K. N. Andreev AU - E. Ya. Khruslov PY - 2015/12/25 Y2 - 2024/03/29 TI - Regularized integrals of motion for the Korteweg – de-Vries equation in the class of nondecreasing functions JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 67 IS - 12 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2093 AB - 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 Cauchy problem, with explicit dependence on time. ER -