Nonlinear tunnelling effect of combined Kuznetsov-Ma soliton in (3+1)-dimensional -symmetric inhomogeneous nonlinear couplers with gain and loss

A (3+1)-dimensional variable-coefficient coupled nonlinear Schrodinger equation in parity-time symmetric inhomogeneous nonlinear couplers with gain and loss is studied, and the -symmetric and -antisymmetric combined Kuznetsov-Ma soliton solutions are obtained via the Darboux transformation method. Nonlinear tunnelling effect of controllable combined Kuznetsov-Ma solitons such as their restraint, maintenance and postpone are discussed when they pass through the dispersion/diffraction barrier and well.