{"paper":{"title":"Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schr\\\"odinger hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th","nlin.SI"],"primary_cat":"cond-mat.supr-con","authors_text":"Daisuke A. Takahashi, Muneto Nitta, Ryosuke Yoshii, Shunji Tsuchiya","submitted_at":"2012-05-15T09:20:13Z","abstract_excerpt":"The chiral Gross-Neveu model or equivalently the linearized Bogoliubov-de Gennes equation has been mapped to the nonlinear Schr\\\"odinger (NLS) hierarchy in the Ablowitz-Kaup-Newell-Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n-th NLS hierarchy generally has n+1 gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3299","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}