Geodesic
The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 414-422

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We construct a set of examples of bottom reliefs for which there exist captured waves corresponding to quasimodes of the wave operator $\nabla D(x,y)\nabla$. 
@article{MZM_1998_64_3_a9,
     author = {V. S. Matveev},
     title = {The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to {Liouville} metrics and waves on water captured by bottom irregularities},
     journal = {Matemati\v{c}eskie zametki},
     pages = {414--422},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a9/}
}
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V. S. Matveev. The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 414-422. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a9/