TY - JOUR
T1 - Bright and dark solitons in the unidirectional long wave limit for the energy transfer on anharmonic crystal lattices
AU - Cisneros-Ake, Luis A.
AU - Solano Peláez, José F.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - 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.
AB - 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.
KW - Dark-gray soliton
KW - Davydov's soliton
KW - NLS–KdV system
KW - Pseudo spectral method
KW - Two-humps dark soliton
UR - http://www.scopus.com/inward/record.url?scp=85013194936&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2017.02.001
DO - 10.1016/j.physd.2017.02.001
M3 - Artículo
SN - 0167-2789
VL - 346
SP - 20
EP - 27
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -