{"paper":{"title":"The Construction of the mKdV Cyclic Symmetric $N$-soliton Solution by the B\\\"{a}cklund Transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Kazuyasu Shigemoto, Masahito Hayashi, Takuya Tsukioka","submitted_at":"2018-05-24T12:41:52Z","abstract_excerpt":"We study group theoretical structures of the mKdV equation. The Schwarzian type mKdV equation has the global M\\\"{o}bius group symmetry. The Miura transformation makes a connection between the mKdV equation and the KdV equation. We find the special local M\\\"{o}bius transformation on the mKdV one-soliton solution which can be regarded as the commutative KdV B\\\"{a}cklund transformation can generate the mKdV cyclic symmetric $N$-soliton solution. In this algebraic construction to obtain multi-soliton solutions, we could observe the addition formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09637","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"}