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We address symmetry breaking bifurcations (SBBs) in the ground-state (GS) anddipole-mode (DM) solitons of the 1D linearly coupled NLS equations, modelingthe propagation of light in a dual-core planar waveguide with the Kerrnonlinearity and two types of PT-symmetric potentials. The PT-symmetricpotential is employed to obtained different types of solutions. A supercriticalpitchfork bifurcation occurs in families of symmetric solutions of both the GSand DM types. A novel feature of the system is interplay between breakings ofthe PT and inter-core symmetries. Stability of symmetric GS and DM modes andtheir asymmetric counterparts, produced by SBBs of both types, is explored viathe linear-stability analysis and simulations. It is found that the instabilityof PT-symmetric solutions takes place prior to the inter-core symmetrybreaking. Surprisingly, stable inter-core-symmetric GS solutions may remainstable while the PT symmetry is broken. Fully asymmetric GS and DM solitons areonly partially stable. Moreover, we construct symmetric and asymmetric GSsolitons under the action of a pure imaginary localized potential, for whichthe SBB is subcritical. These results exhibit that stable solitons can still befound in dissipative systems. Finally, excitations of symmetric and asymmetricGS solitons are investigated by making the potential's parameters or thesystem's coupling constant functions, showing that GS solitons can be convertedfrom an asymmetric shape onto a symmetric one under certain conditions. Theseresults may pave the way for the study of linear and nonlinear phenomena in adual-core planar waveguide with PT potential and related experimental designs.

Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials