Solitons and periodic waves for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics

2020 ◽  
Vol 72 (11) ◽  
pp. 115004
Author(s):  
Dong Wang ◽  
Yi-Tian Gao ◽  
Cui-Cui Ding ◽  
Cai-Yin Zhang
Keyword(s):  
Fluid Dynamics ◽  
Plasma Physics ◽  
Periodic Waves ◽  
Petviashvili Equation

Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wenying Cui ◽  
Yinping Liu ◽  
Zhibin Li
Keyword(s):  
Fluid Dynamics ◽  
Algebraic Method ◽  
Higher Order ◽  
Decomposition Algorithm ◽  
Periodic Waves ◽  
Order Interaction ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation ◽  
Interaction Phenomena

Abstract In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an N-soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

scholarly journals Phase dynamics of periodic waves leading to the Kadomtsev–Petviashvili equation in 3+1 dimensions

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150137 ◽  
Author(s):  
Daniel J. Ratliff ◽  
Thomas J. Bridges
Keyword(s):  
Phase Modulation ◽  
Space Dimension ◽  
Travelling Waves ◽  
Wave Action ◽  
Periodic Waves ◽  
Kp Equation ◽  
Modulation Equation ◽  
Phase Dynamics ◽  
Quantum Vortex ◽  
Petviashvili Equation

The Kadomstev–Petviashvili (KP) equation is a well-known modulation equation normally derived by starting with the trivial state and an appropriate dispersion relation. In this paper, it is shown that the KP equation is also the relevant modulation equation for bifurcation from periodic travelling waves when the wave action flux has a critical point. Moreover, the emergent KP equation arises in a universal form, with the coefficients determined by the components of the conservation of wave action. The theory is derived for a general class of partial differential equations generated by a Lagrangian using phase modulation. The theory extends to any space dimension and time, but the emphasis in the paper is on the case of 3+1. Motivated by light bullets and quantum vortex dynamics, the theory is illustrated by showing how defocusing NLS in 3+1 bifurcates to KP in 3+1 at criticality. The generalization to N >3 is also discussed.

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