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Lump and lump-soliton solutions to the \((2+1)\)-dimensional Ito equation

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Abstract

Based on the Hirota bilinear form of the \((2+1)\)-dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.

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Acknowledgements

The work was supported in part by a university grant XKY2016112 from Xuzhou Institute of Technology, NSFC under the Grants 11371326, 11301331, and 11371086, NSF under the Grant DMS-1664561, and the Distinguished Professorships by Shanghai University of Electric Power and Shanghai Second Polytechnic University.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, Xuzhou Institute of Technology, Xuzhou, 221111, Jiangsu, People’s Republic of China

    **-Yun Yang

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Wen-**u Ma

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China

    Wen-**u Ma

  4. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wen-**u Ma

  5. School of Mathematics and Key Lab for Nonlinear Mathematical Models and Methods, Fudan University, Shanghai, 200433, People’s Republic of China

    Zhenyun Qin

  6. Department of Mathematics, Zhejiang Normal University, **hua, 321004, Zhejiang, People’s Republic of China

    Wen-**u Ma

  7. College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, 200090, People’s Republic of China

    Wen-**u Ma

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  1. **-Yun Yang
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Correspondence to Wen-**u Ma.

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Yang, JY., Ma, WX. & Qin, Z. Lump and lump-soliton solutions to the \((2+1)\)-dimensional Ito equation. Anal.Math.Phys. 8, 427–436 (2018). https://doi.org/10.1007/s13324-017-0181-9

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  • DOI: https://doi.org/10.1007/s13324-017-0181-9

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