Symmetry breaking of solitons in two-dimensional complex potentials

Abstract

Symmetry breaking is reported for continuous families of solitons in the nonlinear Schrödinger equation with a two-dimensional complex potential. This symmetry-breaking bifurcation is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, such symmetry breaking is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel stability properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenvalues and thus exhibit non-reciprocal nonlinear evolutions under random-noise perturbations.

10 pages, 8 figures

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• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
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Cited by in corpus (6)

• Multidimensional dissipative solitons and solitary vortices
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential
• Integrable nonlinear Klein-Gordon systems with $\mathcal{P}\mathcal{T}$ nonlocality and/or space-time exchange nonlocality
• Dynamics of Rogue Waves in the Partially PT-symmetric Nonlocal Davey-Stewartson Systems
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials