Nonautonomous discrete rogue waves and interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients

TL;DR

This paper analytically explores nonautonomous discrete rogue waves in a generalized Ablowitz-Ladik-Hirota lattice with variable coefficients, revealing their complex propagation, localization, and elastic interactions, extending understanding beyond traditional rogue wave models.

Contribution

It introduces new analytical solutions for nonautonomous discrete rogue waves in a variable-coefficient lattice, highlighting their behavior and interactions beyond standard models.

Findings

Rogue waves become localized in time with decreasing tunnel coupling amplitude.

Interactions between rogue waves are elastic.

Results reduce to standard rogue waves when gain/loss is ignored.

Abstract

We analytically investigate the nonautonomous discrete rogue wave solutions and their interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients, which possess complicated wave propagations in time and are beyond the usual discrete rogue waves. When the amplitude of the tunnel coupling coefficient between sites decreases, these nonautonomous discrete rogue wave solutions become localized in time after they propagate over some certain large critical values. Moreover, we find that the interaction between nonautonomous discrete rogue waves is elastic. In particular, these results can reduce to the usual discrete rogue wave solutions when the gain or loss term is ignored.