期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 16, 期 7, 页码 2663-2666出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2010.10.003
关键词
Traveling wave solution; Rational solution; Hirota's bilinear form; Three-soliton condition
类别
资金
- University of South Florida
- State Administration of Foreign Experts Affairs of China
- Ministry of Education of China
We comment on traveling wave solutions and rational solutions to the 3+1 dimensional Kadomtsev-Petviashvili (KP) equations: (u(t) + 6uu(x) + u(xxx))(x) +/- 3u(yy) +/- 3u(zz) = 0. We also show that both of the 3+1 dimensional KP equations do not possess the three-soliton solution. This suggests that none of the 3+1 dimensional KP equations should be integrable, and partially explains why they do not pass the Painleve test. As by-products, the one-soliton and two-soliton solutions and four classes of specific three-soliton solutions are explicitly presented. (C) 2010 Elsevier B.V. All rights reserved.
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