Can parity-time-symmetric potentials support continuous families of non-parity-time-symmetric solitons?

Abstract

For the one-dimensional nonlinear Schroedinger equations with parity-time (PT) symmetric potentials, it is shown that when a real symmetric potential is perturbed by weak PT-symmetric perturbations, continuous families of asymmetric solitary waves in the real potential are destroyed. It is also shown that in the same model with a general PT-symmetric potential, symmetry breaking of PT-symmetric solitary waves do not occur. Based on these findings, it is conjectured that one-dimensional PT-symmetric potentials cannot support continuous families of non-PT-symmetric solitary waves.

19 pages, 3 figures

References in corpus (2)

• Localized modes in ${\chi }^{(2)}$ media with $\PT$-symmetric localized potential
• Nonlinear stationary states in PT-symmetric lattices

Cited by in corpus (1)

• Necessity of PT symmetry for soliton families in one-dimensional complex potentials