Nonlinear Dynamics

, Volume 94, Issue 4, pp 2643–2654 | Cite as

Observation of interaction phenomena for two dimensionally reduced nonlinear models

  • Fu-Hong Lin
  • Jian-Ping Wang
  • Xian-Wei Zhou
  • Wen-Xiu Ma
  • Xing Lü
Original Paper


To study the lump–soliton interaction phenomenon for the (3 + 1)-dimensional nonlinear model with dimensional reduction, interaction solutions have been formulated by combining positive quadratic functions with hyperbolic function in bilinear equations. The collision between lump and soliton has been analyzed and simulated. When the lump is induced by a bounded twin soliton, the rogue wave turns up, which can only be visible at an instant time. Based on the solutions, it is easy to find the amplitude, the place and the arrival time of the rogue waves. The mechanism investigated in this paper may shed some light on the study of rogue waves in oceanography, fluid dynamics and nonlinear optics.


Lump Soliton Rogue wave Oceanography 



This work is supported by the National Key R&D Program of China (2017YFC0820700), the National Natural Science Foundation of China under Grant No. 61602034, the Fundamental Research Funds for the Central Universities of China, the Foundation of Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous Services and the Open Fund of IPOC (BUPT) under Grant No. IPOC2016B008.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Fu-Hong Lin
    • 1
  • Jian-Ping Wang
    • 1
  • Xian-Wei Zhou
    • 1
  • Wen-Xiu Ma
    • 2
    • 3
    • 4
  • Xing Lü
    • 1
    • 5
  1. 1.School of Computer and Communication EngineeringUniversity of Science and Technology BeijingBeijingChina
  2. 2.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  3. 3.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  4. 4.International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical SciencesNorth-West UniversityMmabathoSouth Africa
  5. 5.Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous ServicesBeijingChina

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