TY - JOUR
AU - K. N. Andreev
AU - E. Ya. Khruslov
PY - 2015/12/25
Y2 - 2024/10/04
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 -