Nonlinear waves in a unlimited environment

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

Issue:  Volume 50, № 2

Rubric:  Physics. Mathematical modeling

Annotation:  The existence of periodic stationary excitations in semibounded anharmonic crystals with different signs of nonlinearity is considered. A new simple model is proposed. The mathematical formulation of such a model is a one-dimensional boundary-value problem for the nonlinear Schrödinger equation on the half-axis. The several types of stationary states in depending on the value of the frequency are ob-tained. These stationary states are describe the periodic distributions of the field of excitation in the sys-tem under consideration. It is shown that in media with negative nonlinearity there is one kind of peri-odically distributed states. In media with positive nonlinearity there are two kinds of periodically distributed states. Such states are described by periodic NLSE solutions containing elliptic functions. The expressions determined the frequencies of all the states in an explicit analytical form are obtained. The conditions for their existence are determined.

Keywords:  nonlinear Schrödinger equation, stationary states, surface, nonlinear media, anharmonicity, nonlinear waves.

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