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

TL;DR

This paper classifies and analyzes eight types of spatial solitons in a dual-channel waveguide with cubic-quintic nonlinearity, exploring their stability, transformations, and bifurcations through eigenvalue analysis and simulations.

Contribution

It introduces a comprehensive classification of spatial solitons in a dual-channel waveguide with cubic-quintic nonlinearity, including stability analysis and bifurcation behavior.

Findings

Eight soliton families identified, with stability properties mapped.

Unstable states transform into persistent breathers with complex dynamics.

Stability exchange observed between broad and narrow antisymmetric states.

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.