title: Discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities.
abstract: A class of discrete nonlinear Schrödinger 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 Schrödinger 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.
authors.affiliation: Institute of Physics, Bhubaneswar, Orissa 751005, India.
authors.forename: Avinash
authors.initials: A
authors.lastname: Khare
authors.forename: Kim Ø
authors.initials: KØ
authors.lastname: Rasmussen
authors.forename: Mario
authors.initials: M
authors.lastname: Salerno
authors.forename: Mogens R
authors.initials: MR
authors.lastname: Samuelsen
authors.forename: Avadh
authors.initials: A
authors.lastname: Saxena