Novel localized wave interaction phenomena and dynamics in the generalized discrete Hirota equation via the generalized (2,N − 2)-fold Darboux transformation

Abstract

We investigate the generalized discrete Hirota equation, which is an integrable discrete version of Hirota equation. The generalized [Formula: see text]-fold Darboux transformation (i.e. generalized [Formula: see text]-fold Darboux transformation when [Formula: see text] with two spectral parameters) is presented to derive the novel localized wave interaction solutions. Moreover, some inelastic interaction evolution phenomena of rogue wave and breather are studied graphically. Numerical simulations are used to explore the dynamical behaviors of certain localized wave interaction solutions, which show that their evolutions are stable against a small noise. The results obtained in this paper can be used to find the interaction properties of localized nonlinear waves in nonlinear optics and relevant fields.