TY - JOUR

T1 - PT -symmetric and antisymmetric nonlinear states in a split potential box

AU - Chen, Zhaopin

AU - Li, Yongyao

AU - Malomed, Boris A.

N1 - Publisher Copyright:
© 2018 The Author(s) Published by the Royal Society. All rights reserved.

PY - 2018/7/28

Y1 - 2018/7/28

N2 - 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.

AB - 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.

KW - Dissipation

KW - Gain

KW - Soliton

KW - Stability

KW - Symmetry breaking

UR - http://www.scopus.com/inward/record.url?scp=85048985294&partnerID=8YFLogxK

U2 - 10.1098/rsta.2017.0369

DO - 10.1098/rsta.2017.0369

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AN - SCOPUS:85048985294

SN - 1364-503X

VL - 376

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2124

M1 - 20170369

ER -