{"paper":{"title":"Ermakov-Painlev\\'e II Symmetry Reduction of a Korteweg Capillarity System","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"nlin.SI","authors_text":"Colin Rogers, Peter A. Clarkson","submitted_at":"2017-01-12T05:36:06Z","abstract_excerpt":"A class of nonlinear Schr\\\"odinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-Painlev\\'e II equation which is linked, in turn, to the integrable Painlev\\'e XXXIV equation. A nonlinear Schr\\\"odinger encapsulation of a Korteweg-type capillary system is thereby used in the isolation of such a Ermakov-Painlev\\'e II reduction valid for a multi-parameter class of free energy functions. Iterated application of a B\\\"acklund transformation then allows the construction of novel classes of exact solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03238","kind":"arxiv","version":3},"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"}