Journal
NONLINEAR DYNAMICS
Volume 86, Issue 1, Pages 523-534Publisher
SPRINGER
DOI: 10.1007/s11071-016-2905-z
Keywords
Lump solution; Generalized bilinear operator; Generalized Kadomtsev-Petviashvili-Boussinesq equation
Categories
Funding
- 111 Project of China [B16002]
- National Natural Science Foundation of China [61308018, 11371326, 11271008, 11301454, 11271168]
- China Postdoctoral Science Foundation [2014T70031]
- Fundamental Research Funds for the Central Universities of China [2015JBM111]
- Natural Science Foundation of Shanghai [11ZR1414100]
- Zhejiang Innovation Project of China [T200905]
- First-class Discipline of Universities in Shanghai
- Shanghai University Leading Academic Discipline Project [A13-0101-12-004]
- Distinguished Professorship at Shanghai University of Electric Power
- Natural Science Foundation for Colleges and Universities in Jiangsu Province [13KJD110009]
- Jiangsu Qing Lan Project
- XZIT [XKY 2013202]
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Associated with the prime number p = 3, a combined model of generalized bilinear Kadomtsev-Petviashvili and Boussinesq equation (gbKPB for short) in terms of the function f is proposed, which involves four arbitrary coefficients. To guarantee the existence of lump solutions, a constraint among these four coefficients is presented firstly, and then, the lump solutions are constructed and classified via searching for positive quadratic function solutions to the gbKPB equation. Different conditions posed on lump parameters are investigated to keep the analyticity and rational localization of the resulting solutions. Finally, 3-dimensional plots, density plots and 2-dimensional curves with particular choices of the involved parameters are given to show the profile characteristics of the presented lump solutions for the potential function u = 2(lnf)(x)
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