Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5500280 | Physica D: Nonlinear Phenomena | 2017 | 21 Pages |
Abstract
The problem of energy transportation along a cubic anharmonic crystal lattice, in the unidirectional long wave limit, is considered. A detailed process, in the discrete lattice equations, shows that unidirectional stable propagating waves for the continuum limit produce a coupled system between a nonlinear Schrödinger (NLS) equation and the Korteweg-de Vries (KdV) equation. The traveling wave formalism provides a diversity of exact solutions ranging from the classical Davydov's soliton (subsonic and supersonic) of the first and second kind to a class consisting in the coupling between the KdV soliton and dark solitons containing the typical ones (similar to the dark-gray soliton in the standard defocusing NLS) and a new kind in the form of a two-hump dark soliton. This family of exact solutions are numerically tested, by means of the pseudo spectral method, in our NLS-KdV system.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Luis A. Cisneros-Ake, José F. Solano Peláez,