Abstract
A (3+1)-dimensional coupled nonlinear Schrödinger equation in parity–time symmetric inhomogeneous nonlinear couplers with gain and loss is investigated, and PT-symmetric and PT-antisymmetric superposed Akhmediev breather solutions are derived via the Darboux transformation method. Nonlinear tunnelling for controllable behaviors of the superposed Akhmediev breather is discussed when the superposed Akhmediev breather passes through the diffraction/dispersion barrier and well on an exponential background. Results indicate that the diffraction/dispersion barrier and well have different effects on different types of controllable behaviors of superposed Akhmediev breather. When the restrained and sustained superposed Akhmediev breathers pass through the diffraction/dispersion barrier or well, their amplitudes both magnify or both diminish, respectively, while the postponed Akhmediev breather passes through the diffraction/dispersion barrier or well, its amplitude attenuates or adds, respectively.
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