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Symmetry breaking of solitons in two-dimensional complex potentials
1Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA.
Summary
Symmetry breaking in nonlinear Schrödinger equations is possible with special potentials, leading to asymmetric solitons. These solitons exhibit novel instabilities and nonreciprocal evolutions, challenging previous assumptions.
Area of Science:
- Nonlinear Optics
- Mathematical Physics
- Soliton Dynamics
Background:
- Symmetry breaking is typically forbidden in generic complex potentials for nonlinear Schrödinger equations.
- Partially parity-time-symmetric potentials offer a unique scenario where symmetry breaking can occur.
Purpose of the Study:
- To investigate symmetry breaking in continuous families of solitons within a two-dimensional complex potential.
- To analyze the stability of emerging asymmetric solitons and reveal novel properties.
Main Methods:
- Analysis of nonlinear Schrödinger equation with a specific class of potentials.
- Bifurcation analysis to identify new soliton branches.
- Linear stability analysis to study eigenvalue dynamics.
Main Results:
- Continuous families of solitons exhibit symmetry breaking at a bifurcation point, yielding asymmetric solitons.
- Two novel properties of bifurcated asymmetric solitons were identified: oscillatory instability and nonreciprocal nonlinear evolutions.
- Asymmetric solitons with identical powers can display distinct unstable eigenvalues and behaviors.
Conclusions:
- Partially parity-time-symmetric potentials allow for symmetry breaking in soliton families.
- The study reveals new mechanisms for instability and asymmetric dynamics in solitons.
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