{"paper":{"title":"Efficient determination of the energy landscape of nonlinear Schr\\\"odinger-type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.supr-con","quant-ph"],"primary_cat":"physics.comp-ph","authors_text":"Bart Partoens, Daniele Avitabile, Milorad V. Milo\\v{s}evi\\'c, Nico Schl\\\"omer, Wim Vanroose","submitted_at":"2012-09-26T23:16:11Z","abstract_excerpt":"We describe a systematic approach for the efficient numerical solution of nonlinear Schr\\\"odinger-type partial differential equations of the form $(K +V + g|\\psi|^2)\\psi=0$, with an energy operator $K$, a scalar potential $V$, and a scalar parameter $g$. Instrumental to the approach are developments in numerical linear and nonlinear algebra, specifically numerical parameter continuation. We demonstrate how a continuous sequence of solutions can be obtained regardless of their stability, so that finally the spectrum of stable and unstable solutions in the specified parameter range is fully reve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6094","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":""},"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"}