Modulational instability and higher order-rogue wave solutions for the generalized discrete Hirota equation

This paper investigates the modulational instability and higher order-rogue waves in the generalized discrete Hirota system. The Lax pair and conservation laws for this system are constructed. Then the existent conditions for its modulational instability to form the rogue waves are given starting from the plane wave solution. Furthermore, the higher-order discrete rogue waves of this system are reported using the novel discrete version of generalized perturbation (n,N−n)-fold Darboux transformation. Finally, the dynamical behaviors of the strong and weak interactions of these higher-order discrete rogue waves are discussed analytically and numerically, which exhibits abundant nonlinear wave structures. These results may be useful for understanding some physical phenomena in optical fibers and relevant fields. •The perturbation (n,N−n)-fold Darboux transformation is proposed.•Higher-order discrete rogue waves are obtained.•Modulational instability discrete rogue waves is investigated numerically.