Geodesic
Resonance fenomena in the nonlinear equation of a~proper semiconductor $h^2\Delta u=\operatorname{sh}u$
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 35-44

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A boundary value problem of Steklov type for the non-linear semiconductor equation is discussed. Assuming the existence of closed stable geodesic on the surface of a semiconductor the asymptotic solutions which are concentrated in the vicinity of the geodesic are constructed. The solutions are obtained in terms of eigenfunctions if the Laplace operator on a Riemannian manifold and multi-soliton solutions of the Sine-Gordon equation. Similar results are obtained for the mixed boundary value problem. 
@article{ZNSL_1979_84_a5,
     author = {S. Yu. Dobrokhotov and V. P. Maslov},
     title = {Resonance fenomena in the nonlinear equation of a~proper semiconductor $h^2\Delta u=\operatorname{sh}u$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {35--44},
     publisher = {mathdoc},
     volume = {84},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a5/}
}
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S. Yu. Dobrokhotov; V. P. Maslov. Resonance fenomena in the nonlinear equation of a~proper semiconductor $h^2\Delta u=\operatorname{sh}u$. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 35-44. http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a5/