| Abstract: | One considers a Steklov-type boundary-value problem for the nonlinear equation of a semiconductor. Under the assumption of the existence on the surface of the semiconductor of a closed geodesic, stable in a linear approximation, one constructs asymptotic solutions which are concentrated in the neighborhood of this geodesic. The obtained solutions are expressed in terms of the known asymptotic eigenfunctions of the Laplace operator on a Riemann manifold and in terms of the multisoliton solutions of the Sine-Gordon equation. Similar solutions are obtained for the mixed boundary-value problem. |
