{"paper":{"title":"Inelastic Scattering, Emergent Interactions of Solitons in the Zakharov-Kuznetsov Equation through Conservative and non-Conservative Physics-Informed Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","physics.flu-dyn"],"primary_cat":"nlin.SI","authors_text":"A. Nakamula, K. Obuse, K. Shimasaki, K. Toda, N. Sawado, Y. Shimazaki, Y. Suzuki","submitted_at":"2024-12-28T05:15:59Z","abstract_excerpt":"The Zakharov-Kuznetsov equation, originally a three dimensional mathematical model of plasma with a uniform magnetic field, is a direct extension of the KdV equation into higher dimensions and is a typical quasi-integrable system. Physics-Informed Neural Networks (PINNs) are used to study the collision of soliton solutions in the 2+1 dimensional Zakharov-Kuznetsov equation. PINNs are able to successfully solve the equations in the forward process, and the solutions are obtained using a mesh-free approach and automatic differentiation, taking into account conservation laws. In the inverse proce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20027","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20027/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"}