{"paper":{"title":"A note on the existence of traveling-wave solutions to a Boussinesq system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira","submitted_at":"2014-08-03T12:53:20Z","abstract_excerpt":"We obtain a one-parameter family $$(u_{\\mu}(x,t),\\eta_{\\mu}(x,t))_{\\mu\\geq \\mu_0}=(\\phi_{\\mu}(x-\\omega_{\\mu} t),\\psi_{\\mu}(x-\\omega_{\\mu} t))_{\\mu\\geq \\mu_0}$$ of traveling-wave solutions to the Boussinesq system\n  $$u_t+\\eta_x+uu_x+c\\eta_{xxx}=0,\\eta_t+u_x+(\\eta u)_x+au_{xxx}=0$$\nin the case $a,c<0$, with non-null speeds $\\omega_{\\mu}$ arbitrarily close to $0$ ($\\omega_{\\mu}\\xrightarrow[\\mu\\to+\\infty]{} 0$). We show that the $L^2$-size of such traveling-waves satisfies the uniform (in $\\mu$) estimate $\\|\\phi_{\\mu}\\|_2^2+\\|\\psi_{\\mu}\\|_2^2\\leq C\\sqrt{|a|+|c|},$ where $C$ is a positive constant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0494","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"}