Geodesic
Resonant phenomena in slowly irregular rectangular waveguides
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 173-179

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The waveguide with a rectangular cross section of size and orientation slowly changing along the waveguide's length is considered. Methods of the canonical perturbation theory to describe the ray dynamics in the waveguide are used. As the size and orientation of cross section slowly changes along the ray trajectory, certain resonance conditions can be satisfied. The phenomena of scattering on a resonance and capture into a resonance is studied. These phenomena lead to destruction of adiabatic invariance in the system. 
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     author = {A. P. Itin and A. I. Neishtadt and A. A. Vasil'ev},
     title = {Resonant phenomena in slowly irregular rectangular waveguides},
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     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a15/}
}
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A. P. Itin; A. I. Neishtadt; A. A. Vasil'ev. Resonant phenomena in slowly irregular rectangular waveguides. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 173-179. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a15/