Journal
PHYSICS LETTERS A
Volume 378, Issue 4, Pages 367-373Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2013.11.033
Keywords
PT symmetry; Soliton families; NLS equations
Categories
Funding
- Air Force Office of Scientific Research [USAF 9550-12-1-0244]
- National Science Foundation [DMS-1311730]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1311730] Funding Source: National Science Foundation
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For the one-dimensional nonlinear Schrodinger equation with a complex potential, it is shown that if this potential is not parity-time (PT) symmetric, then no continuous families of solitons can bifurcate out from linear guided modes, even if the linear spectrum of this potential is all real. Both localized and periodic non-PT-symmetric potentials are considered, and the analytical conclusion is corroborated by explicit examples. Based on this result, it is argued that PT-symmetry of a one-dimensional complex potential is a necessary condition for the existence of soliton families. (C) 2013 Elsevier B.V. All rights reserved.
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