2019
Том 71
№ 8

All Issues

Andreev K. N.

Articles: 1
Article (Russian)

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

Andreev K. N., Khruslov E. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1587-1601

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.