2024/12/24 by Ruihong Ma, Ma, Ruihong, Engui Fan +1
Engineering · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Laser-Matter Interactions and Applications #Laser-Plasma Interactions and Diagnostics #Mathematical Physics (math-ph) #Particle Accelerators and Free-Electron Lasers
paper · pdf · doi:10.48550/arxiv.2412.18175
openalex publication_date 2024/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider soliton gas solutions of the modified Korteweg-de Vries (mKdV) equation, where the point spectrum of the condensate is located within a bounded domain in the upper half-plane. We first demonstrate that when the domain is a quadrature and the soliton density is an analytic function, the corresponding deterministic soliton gas coincides with a finite number of solitons, which we call this effect soliton shielding. When the domain is an ellipse and the soliton density is analytic, the corresponding deterministic soliton gas reduces the spectral data to the segment joining the foci. The initial datum of this Cauchy problem is asymptotically step-like oscillatory, described by a periodic elliptic function as \( x → +∞ \), and it vanishes exponentially fast as \( x → -∞ \).