Solitons in PT-symmetric potential with competing nonlinearity

Generalized Darboux Transformation and Rational Solutions for the Nonlocal Nonlinear Schrödinger Equation with the Self-Induced Parity-Time Symmetric Potential

“…In the nonlinear optics, the PT symmetric and Kerr nonlinearity linear potentials have been intensively researched in the nonlinear Schrödinger (NLS) equations. For example, [14] has studied the soliton in PT symmetric potential with competing nonlinearity; [15] has studied the dynamical behaviors of 2D nonautonomous solitons in PT symmetric potentials; and [16] has studied stable dark solitons in PT symmetric dual-core waveguides.…”

Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential

“…In the nonlinear optics, the nonlinear Schrödinger (NLS) equations including the Kerr nonlinearity and PT -symmetric linear potentials have been intensively studied in the past few years [12][13][14][15][16]. For instance, those works include the following aspects: the interactions of bright and dark solitons with a PT -symmetric dipole [13], the effect of competing nonlinearities on beam dynamics in PT -symmetric potentials [12,14], stable dark solitons in PT -symmetric dual-core waveguides [15], and dynamical behaviors in the oligomers [16].…”

“…For instance, those works include the following aspects: the interactions of bright and dark solitons with a PT -symmetric dipole [13], the effect of competing nonlinearities on beam dynamics in PT -symmetric potentials [12,14], stable dark solitons in PT -symmetric dual-core waveguides [15], and dynamical behaviors in the oligomers [16]. However, the complex-valued linear potential usually breaks the integrability of the equation, so that the nonlinear beam dynamics in the presence of PT -symmetric optical potential has been mainly studied by the numerical methods [17,18].…”

Stability of optical solitons in parity-time-symmetric optical lattices with competing cubic and quintic nonlinearities

“…Many works have shown that the competing effect between cubic and quintic nonlinearities plays a significant role in the dynamics of solitons [38][39][40][41][42][43][44][45]. Recently, the competing cubic and quintic nonlinearities have been also applied in the study of optical solitons in PT-symmetric optical systems [46][47][48]. With the help of such competing cubic-quintic nonlinearities, the PT-symmetric optical couplers can support stable twodimensional solitons [46].…”

“…The existence of gap solitons has also been demonstrated in the first band gap of optical PTsymmetric lattices with competing nonlinearity [47]; however, they are not stable. In the presence of a PT-symmetric localized potential (the so-called Scarff potential), the existence and stability of solitons have also been reported with competing cubic and generalized nonlinearity [48].…”