{"paper":{"title":"Long-time asymptotics for the $N_{\\infty}$-soliton solution to the KdV equation with two types of generalized reflection coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Guoqiang Zhang, Zhenya Yan","submitted_at":"2025-02-04T12:33:46Z","abstract_excerpt":"We systematically investigate the long-time asymptotics for the $N_{\\infty}$-soliton solution to the KdV equation in the different regions with the aid of the Riemann-Hilbert (RH) problems with two types of generalized reflection coefficients on the interval $\\left[\\eta_1, \\eta_2\\right]\\in \\mathbb{R}^+$: $r_0(\\lambda,\\eta_0; \\beta_0, \\beta_1,\\beta_2)=\\left(\\lambda-\\eta_1\\right)^{\\beta_1}\\left(\\eta_2-\\lambda\\right)^{\\beta_2}\\left|\\lambda-\\eta_0\\right|^{\\beta_0}\\gamma\\left(\\lambda\\right)$, $r_c(\\lambda,\\eta_0; \\beta_1,\\beta_2)=\\left(\\lambda-\\eta_1\\right)^{\\beta_1}\\left(\\eta_2-\\lambda\\right)^{\\be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02273","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.02273/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"}