Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

Abstract

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. Among the families of trapped beams are symmetric and antisymmetric solitons of "broad" and "narrow" types, composite states, built as combinations of broad and narrow beams with identical or opposite signs ("unipolar" and "bipolar" states, respectively), and "single-sided" broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via eigenvalues of small perturbations, and is verified in direct simulations. Three species - narrow symmetric, broad antisymmetric, and unipolar composite states - are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak inter-channel coupling.

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• Realization of a single Josephson junction for Bose-Einstein condensates
• Spontaneous symmetry breaking of solitons trapped in a double-channel potential
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• Two-Component Nonlinear Schrodinger Models with a Double-Well Potential
• Dark matter-wave solitons in the dimensionality crossover
• All-optical switching in a two-channel waveguide with cubic-quintic nonlinearity

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• Kink-like Solitons in Quantum Droplet
• Generic transverse stability of kink structures in atomic and optical nonlinear media with competing attractive and repulsive interactions
• Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
• Spontaneous symmetry breaking and the dynamics of three interacting nonlinear optical resonators with gain and loss
• Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity