{"paper":{"title":"Lie symmetry analysis and new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"nlin.PS","authors_text":"Dharmendra Kumar, Sachin Kumar","submitted_at":"2018-08-06T07:35:53Z","abstract_excerpt":"Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this article, we construct new solitary wave solutions for the (3+1)-dimensional generalized shallow water wave (GSWW) equation by using Lie symmetry method. A variety of analytic (closed-form) solutions such as new periodic solitary wave, cross-kink soliton and doubly periodic breather-type solutions have been obtained by using invariance of the concerned (3+1)-dimensional GSWW equation under one-parameter Lie group of tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07005","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"}