Analysis and Mathematical Physics

, Volume 8, Issue 3, pp 427–436 | Cite as

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

  • Jin-Yun Yang
  • Wen-Xiu MaEmail author
  • Zhenyun Qin


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.


Bilinear form Lump solution Soliton solution 

Mathematics Subject Classification

35Q51 35Q53 37K40 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematical and Physical SciencesXuzhou Institute of TechnologyXuzhouPeople’s Republic of China
  2. 2.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  3. 3.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  4. 4.International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical SciencesNorth-West University Mafikeng CampusMmabathoSouth Africa
  5. 5.School of Mathematics and Key Lab for Nonlinear Mathematical Models and MethodsFudan UniversityShanghaiPeople’s Republic of China
  6. 6.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China
  7. 7.College of Mathematics and PhysicsShanghai University of Electric PowerShanghaiPeople’s Republic of China

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