期刊
CHAOS SOLITONS & FRACTALS
卷 114, 期 -, 页码 99-107出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2018.06.029
关键词
PT-symmetry; Bilinear method; Breather solution; Rational solution; Semi-rational solution
资金
- NSF of China [11671219]
- K.C. Wong Magna Fund in Ningbo University
- National Science Foundation (US) [2015616]
- Binational Science Foundation (US-Israel) [2015616]
Recently, an integrable system of coupled (2 + 1)-dimensional nonlinear Schrodinger (NLS) equations was introduced by Fokas (Eq. (18) in Nonlinearity 29, 319324 (2016)). Following this pattern, two integrable equations [Eqs. (2) and (3)] with specific parity-time symmetry are introduced here, under different reduction conditions. For Eq. (2), two kinds of periodic solutions are obtained analytically by means of the Hirota's bilinear method. In the long-wave limit, the two periodic solutions go over into rogue waves (RWs) and semi-rational solutions, respectively. The RWs have a line shape, while the semi-rational states represent RWs built on top of the background of periodic line waves. Similarly, semi-rational solutions consisting of a line RW and line breather are derived. For Eq. (3), three kinds of analytical solutions, viz., breathers, lumps and semi-rational solutions, representing lumps, periodic line waves and breathers are obtained, using the Hirota method. Their dynamics are analyzed and demonstrated by means of three-dimensional plots. It is also worthy to note that Eq. (2) can reduce to a (1 + 1)-dimensional reverse-space nonlocal NLS equation by means of a certain transformation, Lastly, main differences between solutions of Eqs. (2) and (3) are summarized. (C) 2018 Elsevier Ltd. All rights reserved.
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