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

  • K. N. Andreev
  • E. Ya. Khruslov Физ.-техн. ин-т низких температур НАН Украины, Харьков


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.
How to Cite
Andreev, K. N., and E. Y. Khruslov. “Regularized Integrals of Motion for the Korteweg – De-Vries Equation in the Class of Nondecreasing Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 12, Dec. 2015, pp. 1587-01,
Research articles