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Exact solutions for a soliton crystal

Dodd, L.R. and Lohe, Max A. (1991). Exact solutions for a soliton crystal. Journal of Mathematical Physics,32(5):1368-1375.

Document type: Journal Article
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Title Exact solutions for a soliton crystal
Author Dodd, L.R.
Lohe, Max A.
Journal Name Journal of Mathematical Physics
Publication Date 1991
Volume Number 32
Issue Number 5
ISSN 0022-2488   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-0347442658
Start Page 1368
End Page 1375
Total Pages 8
Place of Publication United States of America
Publisher A I P Publishing LLC
Abstract A model field theory in one space and one time dimension for a system of fermions interacting through a scalar field with the self-energy density of the linear sigma model is considered. Exact, periodic solutions of the mean field equations for N Nf fermions on a linear lattice of N cells with Nf fermions per cell are found for arbitrarily large N. The multisoliton solutions are expressed entirely in terms of Jacobi elliptic functions and explicit expressions for the fermion energy spectrum and the energy density of the system are given. In the low-density limit the solution in a single cell reduces to the shallow or deep bag solution previously found by Campbell and Liao. Conditions for the bifurcation of the periodic, crystal solutions from solutions with a constant sigma field at high densities are derived, and comparison is made with earlier numerical work.
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Created: Fri, 29 Aug 2014, 20:27:19 CST by Anthony Hornby