{"paper":{"title":"On pattern structures of the N-soliton solution of the discrete KP equation over a finite field","license":"","headline":"","cross_cats":["nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Jonathan J C Nimmo, Mariusz Bialecki","submitted_at":"2006-08-17T07:33:11Z","abstract_excerpt":"The existence and properties of coherent pattern in the multisoliton solutions of the dKP equation over a finite field is investigated. To that end, starting with an algebro-geometric construction over a finite field, we derive a \"travelling wave\" formula for $N$-soliton solutions in a finite field. However, despite it having a form similar to its analogue in the complex field case, the finite field solutions produce patterns essentially different from those of classical interacting solitons."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0608041","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"}