Controllable rogue wave and mixed interaction solutions for the coupled Ablowitz–Ladik equations with branched dispersion

Abstract

Under consideration are the coupled Ablowitz–Ladik lattice equations with branched dispersion, which may be used to model the propagation of an optical field in a tight binding waveguide array. The discrete generalized (m,N−m)-fold Darboux transformation based on 2 × 2 Lax pair is extended to construct rogue wave solutions for this discrete coupled system with 4 × 4 Lax pair. Novel position controllable rogue wave with multi peaks and depressions and mixed interaction structures of breather and rouge wave are shown graphically. It is clearly shown that these new discrete rogue wave structures in this coupled system are different from those of the single component Ablowitz–Ladik equation. These results may be useful to explain some physical phenomena in nonlinear optics.