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Nonlinear Dynamics

, Volume 92, Issue 3, pp 1369–1377 | Cite as

General soliton solutions to a nonlocal long-wave–short-wave resonance interaction equation with nonzero boundary condition

  • Baonan Sun
Original Paper

Abstract

Under investigation in this work is a newly proposed nonlocal long-wave–short-wave resonance interaction (LSRI) equation with the self-induced parity-time (PT) symmetric potential. This equation offers PT symmetry analogues of the classical integrable LSRI equation and may be important for the occurence of such equations in nonlinear optics as the nonlocal NLS equation. General soliton solutions to the nonlocal LSRI equation with nonzero boundary condition are derived by using the Hirota’s bilinear method combined with the Kadomtsev–Petviashvili (KP) hierarchy reduction method. These solutions are expressed in terms of Gramian determinants and include dark–dark solitons, dark–antidark solitons and antidark–antidark solitons. Three typical cases of the two solitons, namely two dark–dark solitons, two dark–antidark solitons and two antidark–antidark solitons, are demonstrated.

Keywords

Nonlocal long-wave–short-wave resonance interaction equation PT symmetry Soliton solution Bilinear transform method 

Notes

Acknowledgements

The author thanks Prof. Y. Zhang for his helpful discussions. This work was supported by the National Key Research and Development Program of China (Grant Nos. 2016YFC1402000, 2016YFC1402304), NSFC–Shandong Joint Fund for Marine Science Research Centers (Grant No. U1606405).

Compliance with ethical standards

Conflict interest

We declare we have no conflict of interests.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Marine Science and Numerical ModelingThe First Institute of OceanographyQingdaoChina
  2. 2.Laboratory for Regional Oceanography and Numerical ModelingQingdao National Laboratory for Marine Science and TechnologyQingdaoChina

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