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arXiv · 1806.11107

Two (2 + 1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions

Yulei Cao·Boris A. Malomed·Jingsong He
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Abstract

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,\textit{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 \textquotedblleft reverse-space" nonlocal NLS equation by means of a certain transformation, Lastly, main differences between solutions of eqs.2 and 3 are summarized.

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Yulei Cao, Boris A. Malomed, Jingsong He. 2018-06-28. Two (2 + 1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions. https://doi.org/10.1016/j.chaos.2018.06.029

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