Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9867836 | Physics Letters A | 2005 | 12 Pages |
Abstract
Instead of using the homoclinic orbit approach, which was commonly taken when studying the localized solutions of the discrete non-linear Schrödinger (DNLS) equation in one-dimensional lattices, we apply the continuation theorem to investigate the existence, stability, and spatial complexity of the localized solutions, including bright breathers, dark breathers, and anti-phase breathers, of the parametrically driven and damped DNLS equation in high-dimensional lattices. In particular, we prove that the sufficient condition that the driving strength exceeds the damping constant is necessary for the system with weak coupling to possess localized solutions.
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Authors
Yu Feng, Wen-Xin Qin, Zhigang Zheng,