{"paper":{"title":"Large-space and long-time asymptotic behaviors of $N_{\\infty}$-soliton solutions (soliton gas) for the focusing Hirota equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","nlin.PS","physics.optics"],"primary_cat":"nlin.SI","authors_text":"Weifang Weng, Zhenya Yan","submitted_at":"2024-01-17T02:15:42Z","abstract_excerpt":"The Hirota equation is one of the integrable higher-order extensions of the nonlinear Schr\\\"odinger equation, and can describe the ultra-short optical pulse propagation in the form $iq_t+\\alpha(q_{xx}+ 2|q|^2q)+i\\beta (q_{xxx}+ 6|q|^2q_x)=0,\\, (x,t)\\in\\mathbb{R}^2\\, (\\alpha,\\,\\beta\\in\\mathbb{R})$. In this paper, we analytically explore the asymptotic behaviors of a soliton gas for the Hirota equation including the complex modified KdV equation, in which the soliton gas is regarded as the limit $N\\to \\infty$ of $N$-soliton solutions, and characterized using the Riemann-Hilbert problem with disc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08924","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.08924/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"}