title: PT-symmetric couplers with competing cubic-quintic nonlinearities.
abstract: We introduce a one-dimensional model of the parity-time ( PT)-symmetric coupler, with mutually balanced linear gain and loss acting in the two cores, and nonlinearity represented by the combination of self-focusing cubic and defocusing quintic terms in each core. The system may be realized in optical waveguides, in the spatial and temporal domains alike. Stationary solutions for PT-symmetric solitons in the systems are tantamount to their counterparts in the ordinary coupler with the cubic-quintic nonlinearity, where the spontaneous symmetry breaking of solitons is accounted for by bifurcation loops. A novel problem is stability of the PT-symmetric solitons, which is affected by the competition of the PT symmetry, linear coupling, cubic self-focusing, and quintic defocusing. As a result, the solitons become unstable against symmetry breaking with the increase of the energy (alias integral power, in terms of the spatial-domain realization), and they retrieve the stability at still larger energies. Above a certain value of the strength of the quintic self-defocusing, the PT symmetry of the solitons becomes unbreakable. In the same system, PT-antisymmetric solitons are entirely unstable. We identify basic scenarios of the evolution of unstable solitons, which may lead to generation of additional ones, while stronger instability creates expanding quasi-turbulent patterns with limited amplitudes. Collisions between stable solitons are demonstrated to be quasi-elastic.
authors.affiliation: Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Morelos 62210, Mexico.
authors.forename: Gennadiy
authors.initials: G
authors.lastname: Burlak
authors.affiliation: Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Morelos 62210, Mexico.
authors.forename: Salomon
authors.initials: S
authors.lastname: Garcia-Paredes
authors.affiliation: Department of Physical Electronics, School of Electric Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed