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Comment on the 3+1 dimensional Kadomtsev–Petviashvili equations

✍ Scribed by Wen-Xiu Ma

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
177 KB
Volume
16
Category
Article
ISSN
1007-5704

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✦ Synopsis

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 Painlevé test. As by-products, the one-soliton and two-soliton solutions and four classes of specific three-soliton solutions are explicitly presented.

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