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Multiple breathers and high-order rational solutions of the new generalized (3+1)-dimensional Kadomtsev–Petviashvili equation
- Source :
- The European Physical Journal Plus. 135
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, we consider a new generalized KP equation which is obtained by adding the extra term $$u_{tz}$$ in the previous equation. Based on these detailed discussions in the previous reference documentations, we know that solitons, breathers, lump waves, and rogue waves are four typical local waves. Therefore, we mainly focus on investigating the multi-soliton solutions, high-order breather solutions, and high-order rational solutions. The high-order breather solutions can be derived by taking complex conjugate parameters in the multi-soliton solutions. Applying the long wave limit method to the multi-soliton solutions, we conclude Theorem 3.1 which can be used directly to obtain high-order rational solutions. Meanwhile, for the case of three-soliton and five-soliton, the elastic interaction solutions among two parallel breathers and one soliton as well as between one breather and one soliton also can be derived, respectively. For all these types of exact solutions, we provide corresponding graphics to illustrate their dynamical characteristics in the end.
- Subjects :
- Physics
Complex conjugate
Breather
One-dimensional space
Mathematical analysis
Complex system
General Physics and Astronomy
Kadomtsev–Petviashvili equation
01 natural sciences
Nonlinear Sciences::Exactly Solvable and Integrable Systems
0103 physical sciences
Soliton
Limit (mathematics)
Rogue wave
010306 general physics
Nonlinear Sciences::Pattern Formation and Solitons
010301 acoustics
Subjects
Details
- ISSN :
- 21905444
- Volume :
- 135
- Database :
- OpenAIRE
- Journal :
- The European Physical Journal Plus
- Accession number :
- edsair.doi...........e4bee9bc914d7deb0cd2afc80b2b9281