Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses

Abstract Since the parity-time-( $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric potentials have been investigated. However, previous studies of $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric Scarf-II potentials. The broken linear $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric ones, but feature similar properties. Our results may suggest new experiments for $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric nonlinear waves in nonlinear nonuniform optical media.