Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities

Details Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities

2006-03-15

arxiv.org/abs/nlin/0603034v2

Phys. Rev. E 74, 16607 (2006)

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1103/PhysRevE.74.016607

A class of discrete nonlinear Schrodinger equations with arbitrarily high order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers and moving solutions, are investigated.

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