{"paper":{"title":"Analysis on an extended Majda--Biello system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Yezheng Li","submitted_at":"2014-07-21T04:35:00Z","abstract_excerpt":"In this paper, we begin with extended Majda--Biello system (BSAB equations): $$ \\left\\{\\begin{array}{l} 0=A_t-DA_3+\\mu A_1+\\Gamma_S B^S_1+\\Gamma_A B_1^A+\\left(AB^S\\right)_x \\\\ 0=B^S_t-B_3^S+\\Gamma_SA_1+\\lambda B_1^S+\\sigma B^A_1+AA_1 \\\\ 0=B^A_t-B_3^A+\\Gamma_A A_1+\\sigma B_1^S-\\lambda B_1^A \\end{array}\\right. $$\n  We conclude global well-posedness in $L^2(\\mathbb{R})\\times L^2(\\mathbb{R})\\times L^2(\\mathbb{R})$ by Brougain's method and the stability of solitary wave solutions by putting it in a framework of generalised KdV type system with three components, where Hamiltonian structure plays an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5371","kind":"arxiv","version":4},"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"}