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Nonlinear Dynamics

, Volume 93, Issue 4, pp 2533–2541 | Cite as

M-lump and interactive solutions to a (3 \({+}\) 1)-dimensional nonlinear system

  • Yan Zhang
  • Yinping Liu
  • Xiaoyan Tang
Original Paper

Abstract

This paper aims at computing M-lump solutions for the \((3+1)\)-dimensional nonlinear evolution equation. These solutions in all directions decline to an identical state obtained by employing the “long wave” limit with respect to the N-soliton solutions which are got by using the direct methods. Subsequently, we discuss the dynamic properties of the M-lump solutions which describe the multiple collisions of lumps. Based on the obtained lump solutions, the lump–kink solutions are also obtained. In addition, the periodic interactive solutions are given.

Keywords

(3 \({+}\) 1)-dimensional nonlinear evolution equation Lump solution Lump–kink solution Interaction 

Notes

Acknowledgements

The work is supported by the National Natural Science Foundation of China (Nos. 11675055 and 11435005) and Shanghai Knowledge Service Platform for Trustworthy Internet of Things (No. ZF1213).

Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest between this manuscript and published articles mostly for technical terms, mathematical expressions and explanations on mathematical terms.

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Copyright information

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

Authors and Affiliations

  1. 1.School of Computer Science and Software EngineeringEast China Normal UniversityShanghaiChina

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