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The DBAR Problem and the Thirring Model
Author(s) -
Villarroel Javier
Publication year - 1991
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1991843207
Subject(s) - thirring model , uniqueness , inverse scattering problem , inverse problem , scattering , inverse , physics , class (philosophy) , riemann hypothesis , mathematical analysis , mathematics , expression (computer science) , mathematical physics , quantum mechanics , computer science , fermion , geometry , artificial intelligence , programming language
We study the Thirring model by means of a DBAR‐Riemann‐Hilbert problem. We undertake a rigorous study for both the direct and the inverse problem on the class of rapidly decaying potentials. This study includes a discussion of the existence and uniqueness of solutions of the direct and inverse problems, a characterization of the solutions, and an explicit expression for the scattering data in terms of initial scattering functions.