Volume 13, Issue 1, February 2006, Pages 111 - 116
The Transition of 2-Dimensional Solitons to 1-Dimensional Ones on Hexagonal Lattices
Betti HARTMANN, Wojtek J ZAKRZEWSKI
Received 3 May 2005, Accepted 15 August 2005, Available Online 1 February 2006.
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- We study solitons arising in a system describing the interaction of a two-dimensional discrete hexagonal lattice with an additional electron field (or, in general, an exciton field). We assume that this interaction is electron-phonon-like. In our previous paper  we have studied the existence of two-dimensional solitons and have found that these solitons exist only if the electron-phonon coupling constant is sufficiently large. In this paper, we report the results of our investigation for small values of this constant, close to its critical value for the existence of solitons. We find that as the coupling decreases the soliton gets very broad and then becomes effectively one-dimensional.
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Cite this article
TY - JOUR AU - Betti HARTMANN AU - Wojtek J ZAKRZEWSKI PY - 2006 DA - 2006/02 TI - The Transition of 2-Dimensional Solitons to 1-Dimensional Ones on Hexagonal Lattices JO - Journal of Nonlinear Mathematical Physics SP - 111 EP - 116 VL - 13 IS - 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2006.13.1.9 DO - https://doi.org/10.2991/jnmp.2006.13.1.9 ID - HARTMANN2006 ER -