Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation

• Published in: Communications on pure and applied mathematics Vol. 76; no. 11; pp. 3233 - 3299
• Main Authors: Girotti, Manuela, Grava, Tamara, Jenkins, Robert, McLaughlin, Ken T‐R, Minakov, Alexander
• Format: Journal Article
• Language: English
• Published: New York John Wiley and Sons, Limited 01.11.2023
• Subjects: Kinetic equations; Solitary waves

We analyse the case of a dense modified Korteweg–de Vries (mKdV) soliton gas and its large time behaviour in the presence of a single trial soliton. We show that the solution can be expressed in terms of Fredholm determinants as well as in terms of a Riemann–Hilbert problem. We then show that the so...