Lump and lump-soliton solutions to the \((2+1)\)-dimensional Ito equation
- 646 Downloads
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.
KeywordsBilinear form Lump solution Soliton solution
Mathematics Subject Classification35Q51 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.
- 18.Chakravarty, S., Kodama, Y.: Line-soliton solutions of the KP equation. In: Nonlinear and Modern Mathematical Physics, AIP Conference Proceedings, 1212, pp. 312–341. American Institute of Physics, Melville, NY (2010)Google Scholar
- 34.Ma, W.X.: Generalized bilinear differential equations. Stud. Nonlinear Sci. 2(4), 140–144 (2011)Google Scholar