Recurrence behavior for controllable excitation of rogue waves in a two-dimensional $$\varvec{\mathcal {PT}}$$ PT -symmetric coupler

Abstract

A (2 + 1)-dimensional variable-coefficient coupled nonlinear Schrodinger equation with different diffractions in parity-time symmetric coupler is studied, and exact solutions in the form of two-component Peregrine solution and rogue wave triplet are derived. Based on these solutions, by adjusting the relation between the maximal value \(Z_\mathrm{m}\) and the exciting location values \(Z_0\) for Peregrine solution and \(Z_1,Z_2\) for rogue wave triplet, recurrence behaviors for controllable excitation of Peregrine solution and rogue wave triplet including complete excitation, peak excitation, rear excitation and initial excitation are discussed in the exponential diffraction decreasing system. This phenomenon of recurrence for controllable excitation is owing to different values of diffractions in two transverse directions.