{"paper":{"title":"Loop-type geometric folding of exact solutions of shifted nonlocal NLS and MKdV equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Asl{\\i} Pekcan","submitted_at":"2026-07-12T18:22:53Z","abstract_excerpt":"Based on the notion of foldon, we introduce a geometric framework for constructing folded parametric wave representations of exact solutions of some shifted nonlocal nonlinear Schr\\\"{o}dinger and modified Korteweg-de Vries equations. Unlike the method of constructing loops in $(2+1)$-dimensional integrable models based on universal variable separation approach or hodograph transformation, we consider a simplified geometric approach of constructing loop-type folded profiles via non-monotonic parametrization of the spatial coordinate associated with the exact solution of the $(1+1)$-dimensional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10870","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10870/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}