$${\mathcal {PT}}$$ PT -symmetric and $${\mathcal {PT}}$$ PT -antisymmetric superposed breathers in (3 $$+$$ + 1)-dimensional inhomogeneous nonlinear couplers with balanced gain and loss

Abstract

We discuss a (3+1)-dimensional variable-coefficient coupled nonlinear Schrodinger equation with different diffractions and dispersion in parity-time (\({\mathcal {PT}}\)) symmetric inhomogeneous nonlinear couplers with balanced gain and loss, and derive \({\mathcal {PT}}\)-symmetric and \({\mathcal {PT}}\)-antisymmetric superposed breather and crossing two-breather solutions. The recurrence of controllable superposed breathers including restraint, maintenance and postpone is firstly reported in the dispersion/diffraction decreasing system. This recurrence of controllable behaviors originates from different diffractions and dispersion of systems. Moreover, controllable excitations including restraint, maintenance and postpone of crossing two breathers are also studied in the dispersion/diffraction decreasing system.