Comment on the 3+1 dimensional Kadomtsev-Petviashvili equations

被引：91

作者：

Ma, Wen-Xiu ^{[1
]}

机构：

[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2011年 / 16卷 / 07期

关键词：

Traveling wave solution; Rational solution; Hirota's bilinear form; Three-soliton condition; TRAVELING-WAVE SOLUTIONS; (2+1)-DIMENSIONAL BOUSSINESQ EQUATION; HIROTA 3-SOLITON CONDITION; KP EQUATION; BILINEAR EQUATIONS; EXPLICIT; SOLITONS; SEARCH;

D O I：

10.1016/j.cnsns.2010.10.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2663 / 2666

页数：4

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