2013/05/30 by Zhihui Xie, Xie, Zhihui
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1305.7240
openalex publication_date 2013/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the derivation of a certain type of NLS from many-body interactions of bosonic particles. We consider a model with a finite linear combination of n-body interactions, where n ≥ 2 is an integer. We show that the k-particle marginal density of the BBGKY hierarchy converges when particle number goes to infinity, and the limit solves a corresponding infinite Gross-Pitaevskii hierarchy. We prove the uniqueness of factorized solution to the Gross-Pitaevskii hierarchy based on a priori space time estimates. The convergence is established by adapting the arguments originated or developed in \citeESY, \citeKSS and \citeCPquintic. For the uniqueness part, we expand the procedure followed in \citeKM by introducing a different board game argument to handle the new contraction operator. This new board game argument helps us obtain a good estimate on the Duhamel terms. In \citeKM, the relevant space time estimates are assumed to be true, while we give a prove for it.