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Families of rational solutions of the y-nonlocal Davey–Stewartson II equation

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Abstract

The y-nonlocal Davey–Stewartson II equation is an extension of the usual DS II equation involving a partially parity-time-symmetric potential only with respect to the spatial variable y. By using the Hirota bilinear method, families of n-order rational solutions are obtained, which include lumps in the (x, y)-plane and the (y, t)-plane, growing-and-decaying line waves in the (x, t)-plane, and hybrid solutions of interacting line rogue waves and lumps in the (x, y)-plane.

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Acknowledgements

This work is supported by the NSF of China under Grant No. 11671219 and the K. C. Wong Magna Fund in Ningbo University. Yaobin Liu is supported by the Scientific Research Foundation of Graduate School of Ningbo University. We thank other members in our group at Ningbo University and Mr. Jiguang Rao at USTC (Hefei) for their many discussions and suggestions on the manuscript.

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  1. Department of Mathematics, Ningbo University, Zhejiang, 315211, People’s Republic of China

    Yaobin Liu & Jingsong He

  2. Horia Hulubei National Institute for Physics and Nuclear Engineering, MG–6, 077125, Magurele, Romania

    Dumitru Mihalache

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Liu, Y., Mihalache, D. & He, J. Families of rational solutions of the y-nonlocal Davey–Stewartson II equation. Nonlinear Dyn 90, 2445–2455 (2017). https://doi.org/10.1007/s11071-017-3812-7

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