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Can Parity‐Time‐Symmetric Potentials Support Families of Non‐Parity‐Time‐Symmetric Solitons?
Author(s) -
Yang Jianke
Publication year - 2014
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12032
Subject(s) - parity (physics) , physics , nonlinear system , symmetry (geometry) , quantum mechanics , mathematical physics , classical mechanics , mathematics , geometry
For the one‐dimensional nonlinear Schrödinger 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 does 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.

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