Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

Details Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

2004-09-27

arxiv.org/abs/nlin/0409057v1

Journal of Physics A (Mathematical and General), 38, 807-814 (2005)

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1088/0305-4470/38/4/002

Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that the effective Peierls-Nabarro barrier potential is nonzero thereby indicating that this discrete model is quite likely nonintegrable.

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