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May/June 2015 Derivation of a nonlinear Schrödinger equation with a general power-type nonlinearity in $d=1,2$
Zhihui Xie
Differential Integral Equations 28(5/6): 455-504 (May/June 2015).

Abstract

In this paper, we study the derivation of a certain type of NLS from many-body interactions of bosonic particles in $d=1,2$. We consider a model with a finite linear combination of $n$-body interactions and obtain that the $k$-particle marginal density of the BBGKY hierarchy converges when particle number goes to infinity. Moreover, 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 [6], [15] and [2]. For the uniqueness part, we expand the procedure in [16] by introducing a different board game argument to handle the factorial in the number of terms from Duhamel expansion. The space time bound assumption in [16] is removed in our proof.

Citation

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Zhihui Xie. "Derivation of a nonlinear Schrödinger equation with a general power-type nonlinearity in $d=1,2$." Differential Integral Equations 28 (5/6) 455 - 504, May/June 2015.

Information

Published: May/June 2015
First available in Project Euclid: 30 March 2015

zbMATH: 1363.35358
MathSciNet: MR3328130

Subjects:
Primary: 35Q55 , 81V70

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 5/6 • May/June 2015
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