Theoretical study of resonance of the Kadomtsev–Petviashvili equation

Duan, Wen-Shan; Shi, Yu-Ren; Hong, Xue-Ren

doi:10.1016/j.physleta.2003.12.057

Cited by 39 publications

(21 citation statements)

References 9 publications

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“…Ref. [4] have studied the two sam amplitude soliton resonance of the KP equation, and theoretically predict that the maximum amplitude is 4 times of the initial interacting soliton, which is agree with experiments. This phenomena has been reported in the fluid dynamics [5,6], and in the plasma physics [7][8][9][10][11][12].…”

Section: Introductionsupporting

confidence: 66%

“…Therefore, to solve the KP equation is one of the interesting problems nowadays. Since one and two arbitrary soliton solutions have been obtained analytically until now [4]. Here, in this paper, we want to study the three soliton solution analytically and find the characteristic of the interaction and the resonance phenomena among these three solitons.…”

Section: Introductionmentioning

confidence: 99%

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Interaction and resonance phenomena of multi-soliton

2006

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As is well known, Korteweg-de Vries equation is a typical one which has planar solitary wave. By considering higher order transverse disturbance to planar solitary waves, we study a Kadomtsev-Petviashvili (KP) equation and find some interesting results. In this letter we investigate the three soliton interaction and their resonance phenomena of KP equation, and theoretically find that the maximum amplitude is 9 times of the initial interacting soliton for three same amplitude solitons. Three arbitrary amplitude soliton interaction of KP equation is also studied by numerical simulation, which can also results in resonance phenomena.

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Section: Introductionsupporting

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Interaction and resonance phenomena of multi-soliton

2006

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“…Analyses based on the study of equation (6) derived from equation (5) after the coordinate transform below: [20] In the present study, theories of oblique nonlinear interactions based on the KP equation (equation (7)) are extended to ISWs. For completeness, the following theory is revised from Freeman [1980] and Duan et al [2004]. For equation (7), a soliton solution can be written by changing the dependent variable u into v via…”

Section: Model Equation For the Propagation And Interaction Of Iswsmentioning

confidence: 99%

“…[22] To satisfy the KP equation (equation (7)), the so-called phase shift parameter A is determined as [Duan et al, 2004] …”

Section: Theory Of Resonant Oblique Interactionmentioning

confidence: 99%

Interaction and generation of long-crested internal solitary waves in the South China Sea

Chen¹,

Liu²,

Wang³

et al. 2011

J. Geophys. Res.

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[1] Oblique nonlinear interactions based on the Kadomtsev-Petviashvili equation (also known as the two-dimensional Korteweg-de Vries equation) are extended to internal solitary waves (ISWs) to explain why the amplitude does not decrease owing to the geometric spreading of the cylindrical wavefronts in the South China Sea (SCS). This resonance theory is used to explain a satellite image exhibiting special features, and it is proposed that wave arcs of different amplitude resonate, providing a mechanism for reinforcing a wave by boosting the amplitude. The present theory suggests the amplitude of the ISW that propagates across the SCS basin depends on the interaction of ISWs originating from different sources; hence, studying the generation of an ISW from a single source location cannot predict the ISW correctly.

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“…Duan et al (2004) have studied the resonance of the KP equation, theoretically. The stationary solution of (19) can be written as (Gill et al 2006)…”

Section: The Derivation Of the Kp Equationmentioning

confidence: 99%

Soliton energy of the Kadomtsev–Petviashvili equation in warm dusty plasma with variable dust charge, two-temperature ions, and nonthermal electrons

Pakzad

2009

Astrophys Space Sci

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The propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ions, and nonthermal electrons is studied. By using the reductive perturbation theory, the Kadomtsev-Petviashivili (KP) equation is derived. The energy of the soliton has been calculated. By using standard normal modes analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the energy of the soliton and the angular frequency of the linear wave are also discussed. It is shown that the amplitude of solitary waves of the KP equation diverges at the critical values of plasma parameters. We derive solitons of a modified KP equation with finite amplitude in this situation.

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Theoretical study of resonance of the Kadomtsev–Petviashvili equation

Cited by 39 publications

References 9 publications

Interaction and resonance phenomena of multi-soliton

Interaction and resonance phenomena of multi-soliton

Interaction and generation of long-crested internal solitary waves in the South China Sea

Soliton energy of the Kadomtsev–Petviashvili equation in warm dusty plasma with variable dust charge, two-temperature ions, and nonthermal electrons

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