{"paper":{"title":"Perturbation of Riemann-Hilbert jump contours: smooth parametric dependence with application to semiclassical focusing NLS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Sergey Belov, Stephanos Venakides","submitted_at":"2011-08-25T20:49:24Z","abstract_excerpt":"A perturbation of a class of scalar Riemann-Hilbert problems (RHPs) with the jump contour as a finite union of oriented simple arcs in the complex plane and the jump function with a $z\\log z$ type singularity on the jump contour is considered. The jump function and the jump contour are assumed to depend on a vector of external parameters $\\vec\\beta$. We prove that if the RHP has a solution at some value $\\vec\\beta_0$ then the solution of the RHP is uniquely defined in a some neighborhood of $\\vec\\beta_0$ and is smooth in $\\vec\\beta$. This result is applied to the case of semiclassical focusing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5197","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"}