title: Discrete rogue waves of the Ablowitz-Ladik and Hirota equations.
abstract: We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation.
authors.affiliation: The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors.forename: Adrian
authors.initials: A
authors.lastname: Ankiewicz
authors.forename: Nail
authors.initials: N
authors.lastname: Akhmediev
authors.forename: J M
authors.initials: JM
authors.lastname: Soto-Crespo