On the Form of Dispersive Shock Waves of the Korteweg-de Vries Equation

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2016
• Main Authors: Egorova, I., Gladka, Z., Teschl, G.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/140545
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the Form of Dispersive Shock Waves of the Korteweg-de Vries Equation / I. Egorova, Z. Gladka , G. Teschl // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 1. — С. 3-16. — Бібліогр.: 23 назв. — англ.

We show that the long-time behavior of solutions to the Korteweg{de Vries shock problem can be described as a slowly modulated one-gap solution in the dispersive shock region. The modulus of the elliptic function (i.e., the spectrum of the underlying Schrödinger operator) depends only on the size of...