Rogue-wave solutions for a discrete Ablowitz-Ladik equation with variable coefficients for an electrical lattice

We investigate a discrete Ablowitz-Ladik equation with variable coefficients, which models the modulated waves in an electrical lattice. Employing the similarity transformation and Kadomtsev-Petviashvili hierarchy reduction, we obtain the rogue-wave solutions in the Gram determinant form under certain variable-coefficient constraints. We graphically study the rogue waves with the influence of the coefficient of tunnel coupling between the sites, , time-modulated effective gain/loss term, , space-time-modulated inhomogeneous frequency shift, (), and lattice spacing, h, where t is the scaled time. Increasing value of h leads to the decrease in the rogue waves' amplitudes. Properties of the rogue waves with as the polynomial, sinusoidal, hyperbolic and exponential functions are discussed, respectively. The monotonically increasing, monotonically decreasing, periodic and Gaussian backgrounds are, respectively, displayed with the different . The first-order rogue wave exhibits one hump and two valleys, and the second-order rogue waves exhibit three humps and one highest peak. The third-order rogue waves with the six humps and one highest peak are also presented.