PT -symmetric and antisymmetric nonlinear states in a split potential box

Zhaopin Chen, Yongyao Li, Boris A. Malomed*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce a one-dimensional PT -symmetric system, which includes the cubic self-focusing, a double-well potential in the form of an infinitely deep potential box split in the middle by a delta-functional barrier of an effective height ϵ, and constant linear gain and loss, Y, in each half-box. The system may be readily realized in microwave photonics. Using numerical methods, we construct PT -symmetric and antisymmetric modes, which represent, respectively, the system's ground state and first excited state, and identify their stability. Their instability mainly leads to blowup, except for the case of ϵ =0, when an unstable symmetric mode transforms into a weakly oscillating breather, and an unstable antisymmetric mode relaxes into a stable symmetric one. At ϵ > 0, the stability area is much larger for the PT -antisymmetric state than for its symmetric counterpart. The stability areas shrink with increase of the total power, P. In the linear limit, which corresponds to P→0, the stability boundary is found in an analytical form. The stability area of the antisymmetric state originally expands with the growth of y , and then disappears at a critical value of y.

Original languageEnglish
Article number20170369
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2124
StatePublished - 28 Jul 2018


  • Dissipation
  • Gain
  • Soliton
  • Stability
  • Symmetry breaking


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