期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 67, 期 -, 页码 480-491出版社
ELSEVIER
DOI: 10.1016/j.cnsns.2018.07.020
关键词
Kadomtsev-Petviashvili I equation; KP hierarchy reduction method; Breathers; Lumps; Semi-rational solutions
类别
资金
- Research Program for University in Shandong Province (Natural Science) [J18KA237]
- Doctoral Scientific Research Foundation of Shandong Technology and Business University [BS201703]
- Shandong Provincial Natural Science Foundation [ZR2018MA004]
In this work we derive families of explicit breather solutions of any order to the Kadomtsev-Petviashvili equation (KPI) and the Boussinesq equation. We employ the Hirota bilinear method combined with the KP hierarchy reduction method to determine these solutions. By taking a long wave limit of breather solutions, two types of semi-rational solutions to the KPI equation are constructed via using the determinant expression. The first type of semi-rational solutions only consists of breathers of arbitrary order and lumps of arbitrary order in the (x, y)-plane. The second type of semi-rational solutions comprises of solitons of arbitrary order, breathers of arbitrary order and lumps of arbitrary order in the (x, y)-plane. (C) 2018 Elsevier B.V. All rights reserved.
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