2024/08/25 by Robert P. Jenkins, Jenkins, Robert, Alexander Tovbis +1
Mathematics · Physics and Astronomy · #35Q15 #35Q55 #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2408.13700
openalex publication_date 2024/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we approximate the thermodynamic limit of finite-gap solutions to any integrable equations in the focusing NLS hierarchy (fNLS, mKdV, ...) with an associated multisoliton solutions using the Riemann-Hilbert Problem approach. Moreover, we show that both the finite-gap and multisoliton solutions are approximated in the thermodynamic limit by a generalization of the primitive potentials introduced by V. Zakharov and his collaborators in the KdV context. Under certain assumptions on the spectral data for the finite gap potentials, we provide error estimates for the approximation on compact subsets of the (x,t)-plane.