@article{Andreev_Khruslov_2015, title={Regularized integrals of motion for the Korteweg – de-Vries equation in the class of nondecreasing functions}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2093}, abstractNote={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.}, number={12}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Andreev, K. N. and Khruslov, E. Ya.}, year={2015}, month={Dec.}, pages={1587-1601} }