The asymptotic eigenfunctions of the operator \(\nabla D(x,y)\nabla\) corresponding to Liouville metrics and waves on water captured by bottom irregularities

DOI10.1007/BF02314845zbMath0926.35103MaRDI QIDQ1290815

Vladimir S. Matveev

Publication date: 3 June 1999

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

geodesic flowquasimodesbottom reliefsLiouville torus

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Wave equation (35L05)

Related Items (5)

Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves ⋮ Asymptotics of waves on the shallow water generated by spatially-localized sources and trapped by underwater ridges ⋮ Nonlinear long standing waves with support bounded by caustics or localized in the vicinity of a two-link trajectory ⋮ Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics ⋮ Asymptotic eigenfunctions of the operator \(\nabla D(x)\nabla\) defined in a two-dimensional domain and degenerating on its boundary and billiards with semi-rigid walls

Cites Work

• Unnamed Item
• Nonstandard characteristics and Maslov's operational method in linear problems concerning unsteady water waves
• Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
• Orbital isomorphisms of Liouville systems on a two-dimensional torus

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