2025/02/20 by Aikaterini Gkogkou, Gkogkou, Aikaterini, Guido Mazzuca +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2502.14749
openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
In this work, we carry out a rigorous analysis of a multi-soliton solution of the focusing nonlinear Schrödinger equation as the number, N, of solitons grows to infinity. We discover configurations of N-soliton solutions which exhibit the formation (as N → ∞) of a soliton gas condensate. Specifically, we show that when the eigenvalues of the Zakharov - Shabat operator for the NLS equation accumulate on two bounded horizontal segments in the complex plane with norming constants bounded away from 0, then, asymptotically, the solution is described by a rapidly oscillatory elliptic-wave with constant velocity, on compact subsets of (x,t). We then consider more complex solutions with an extra soliton component, and provide rigorous justification of the predictions of the kinetic theory of solitons in this deterministic setting. This is to be distinguished from previous analyses of soliton gasses where the norming constants were tending to zero with N, and the asymptotic description only included elliptic waves in the long-time asymptotics.