2017
Том 69
№ 9

All Issues

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

Andreev K. N., Khruslov E. Ya.


Abstract

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.

Citation Example: Andreev K. N., Khruslov E. Ya. Regularized integrals of motion for the Korteweg – de-Vries equation in the class of nondecreasing functions // Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1587-1601.