Surface states in nonlinear half-space

Author(s):  S.E. Savotchenko, Dr., Prof., Belgorod State Technological University named after V.G. Shukhov, Belgorod, Russia, savotchenkose@mail.ru

Issue:  Volume 50, №1

Rubric:  Physics

Annotation:  The problems of the existence of surface vibrational states in semibounded anharmonic crystals with different signs of nonlinearity are considered. A model is proposed whose mathematical formulation is a one-dimensional boundary-value problem for the nonlinear Schrödinger equation on the half-axis. In the system under consideration, depending on the frequency value, several types of stationary vi-brational states are obtained that describe local excitations near the surface. Dispersion relations that determine the frequencies of such states are obtained. In limiting cases, expressions for the frequency of stationary vibrational states are obtained in explicit form

Keywords:  nonlinear Schrödinger equation, surface, soliton, localized states

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