2005/12/13 by G. Kalosakas · 1 citation
Computer Science · Physics and Astronomy · #Advanced Fiber Laser Technologies #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #nlin.PS #physics.optics
paper · pdf · doi:10.1016/j.physd.2005.12.023
34 pages, 12 figures
arxiv created 2005/12/13 · openalex publication_date 2006/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.