Geodesic
Open waveguides in a thin Dirichlet lattice: II. Localized waves and radiation conditions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 237-254

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Wave processes localized near an angular open waveguide obtained by thickening two perpendicular semi-infinite rows of ligaments in a thin square lattice of quantum waveguides (Dirichlet problem for the Helmholtz equation) are investigated. Waves of two types are discovered: the first are observed near the lattice nodes and almost do not affect the ligaments, while the second, on the contrary, excite oscillations in the ligaments, whereas the nodes stay relatively at rest. Asymptotic representations of the wave fields are derived, and radiation conditions are imposed on the basis of the Umov-Mandelstam energy principle. 
@article{ZVMMF_2017_57_2_a2,
     author = {S. A. Nazarov},
     title = {Open waveguides in a thin {Dirichlet} lattice: {II.} {Localized} waves and radiation conditions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {237--254},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a2/}
}
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S. A. Nazarov. Open waveguides in a thin Dirichlet lattice: II. Localized waves and radiation conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 237-254. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a2/