{"paper":{"title":"Surface shear waves in a half-plane with depth-variant structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Alexander Shuvalov, Andrey Sarychev, Marco Spadini","submitted_at":"2018-10-15T12:06:30Z","abstract_excerpt":"We consider the propagation of surface shear waves in a half-plane, whose shear modulus $\\mu(y)$ and density $\\rho(y)$ depend continuously on the depth coordinate $y$. The problem amounts to studying the parametric Sturm-Liouville equation on a half-line with frequency $\\omega$ and wave number $k$ as the parameters. The Neumann (traction-free) boundary condition and the requirement of decay at infinity are imposed. The condition of solvability of the boundary value problem determines the dispersion spectrum $\\omega(k)$ for the corresponding surface wave. We establish the criteria for non-exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06294","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"}