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

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

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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

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