One- and two-dimensional bright solitons in inhomogeneous defocusing nonlinearities with an antisymmetric periodic gain and loss

We address that various branches of bright solitons exist in a spatially inhomogeneous defocusing nonlinearity with an imprinted antisymmetric periodic gain-loss profile. The spectra of such systems with a purely imaginary potential never become complex and thus the parity-time symmetry is unbreakable. The mergence between pairs of soliton branches occurs at a critical gain-loss strength, above which no soliton solutions can be found. Intriguingly, which pair of soliton branches will merge together can be changed by varying the modulation frequency of gain and loss. Most branches of one-dimensional solitons are stable in wide parameter regions. We also provide the first example of two-dimensional bright solitons with unbreakable parity-time symmetry.