Multi-peaked localized states of DNLS in one and two dimensions
arXiv:nlin/0512028 · doi:10.1016/j.physd.2005.12.023
Abstract
Multi-peaked localized stationary solutions of the discrete nonlinear Schrodinger (DNLS) equation are presented in one (1D) and two (2D) dimensions. These are excited states of the discrete spectrum and correspond to multi-breather solutions. A simple, very fast, and efficient numerical method, suggested by Aubry, has been used for their calculation. The method involves no diagonalization, but just iterations of a map, starting from trivial solutions of the anti-continuous limit. Approximate analytical expressions are presented and compared with the numerical results. The linear stability of the calculated stationary states is discussed and the structure of the linear stability spectrum is analytically obtained for relatively large values of nonlinearity.
34 pages, 12 figures
References in corpus (6)
- Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
- On classification of intrinsic localized modes for the Discrete Nonlinear Schrödinger Equation
- Standing wave instabilities in a chain of nonlinear coupled oscillators
- Controlled switching of discrete solitons in waveguide arrays
- Charge transport in poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers
- Mobile Localization in nonlinear Schrodinger lattices
Cited by in corpus (4)
- Multipole-mode surface solitons
- Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schrödinger lattices
- Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach
- Floquet solitons in square lattices: Existence, Stability and Dynamics