期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 264, 期 4, 页码 2633-2659出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2017.10.033
关键词
Soliton; Integrable equation; Hirota bilinear form; Lump solution
类别
资金
- NSFC [11371326, 11271008, 11301331, 11371086]
- NSF [DMS-1664561]
- Xuzhou Institute of Technology [XKY2016112]
- Natural Science Fund for Colleges and Universities of Jiangsu Province [17KJB110020]
- Shanghai University of Electric Power and Shanghai Second Polytechnic University
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1664561] Funding Source: National Science Foundation
Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(lnf)(x) and u = 2(lnf)(xx), where xis one spatial variable. Applications are made for a few generalized KP and BKP equations. (C) 2017 Elsevier Inc. All rights reserved.
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