Fermionic approach to soliton equations

In this paper we exploit the algebraic structure of the soliton equations and find solutions in terms of fermion particles. We show how determinants arise naturally in the fermionic approach to soliton equations. We write the τ-function for charged free fermions in terms of determinants. Examples of...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 380; no. 2; pp. 782 - 793
Main Author Ünal, Metin
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.08.2011
Elsevier
Subjects
Algebra
Exact sciences and technology
Fermion particles
General algebraic systems
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Sciences and techniques of general use
Soliton equations
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Soliton equations
Fermion particles
Algebraic structure
Mathematical analysis
Determinant
Algebraic equation
Soliton
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Summary:In this paper we exploit the algebraic structure of the soliton equations and find solutions in terms of fermion particles. We show how determinants arise naturally in the fermionic approach to soliton equations. We write the τ-function for charged free fermions in terms of determinants. Examples of how to get soliton, rational and dromion solutions from τ-functions for the various soliton equations are given.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.03.012