Dynamics of the breather waves, rogue waves and solitary waves in an extend Kadomtsev–Petviashvili equation

Zou, Li; Yu, Zongbing; Wang, Xiu‐Bin

doi:10.1016/j.aml.2018.03.017

Cited by 15 publications

(4 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e wave v 1 given via solution (13) would be closing to a point 2p as t ⟶ + ∞, and it would be closing to a point − 2p as t ⟶ − ∞. While the wave v 2 given via solution (14) would also be closing to a point 2p as t ⟶ + ∞, and it would be closing to a point − 2p as t ⟶ − ∞.…”

Section: Breather Wave Solutions Of the (2 + 1)-dimensional Kdv4 Equa...mentioning

confidence: 98%

“…Tao presented abundant soliton wave solutions for the (3 + 1)-dimensional variable-coefficient nonlinear wave equation in [12] by considering the Hirota bilinear operators. Meanwhile, breather waves and rouge waves also have attracted growing attention on both experimental observations and theoretical predictions [13,14]. ese giant wave phenomena have been found in different fields such as the plasmas, deep ocean, nonlinear optic, biophysics, and even finance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Breather Wave and Traveling Wave Solutions for A (2 + 1)-Dimensional KdV4 Equation

Tao

2022

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this paper, an integrable (2 + 1)-dimensional KdV4 equation is considered. By considering variable transformation and Bell polynomials, an effective and straightforward way is presented to derive its bilinear form. The homoclinic breather test method is employed to construct the breather wave solutions of the equation. Then, the dynamic behaviors of breather waves are discussed with graphic analysis. Finally, the G ′ / G 2 expansion method is employed to obtain traveling wave solutions of the (2 + 1)-dimensional integrable KdV4 equation, including trigonometric solutions and exponential solutions.

show abstract

Section: Breather Wave Solutions Of the (2 + 1)-dimensional Kdv4 Equa...mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Breather Wave and Traveling Wave Solutions for A (2 + 1)-Dimensional KdV4 Equation

Tao

2022

Advances in Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…The problem of wave-wave interaction is a very important one in the earth fluid, and further study can deepen people's understanding of large-scale motion phenomena in the atmosphere, ocean and large lakes. There are many motion equations describing Rossby waves in a layer of fluid, such as one-dimensional KdV equation [13], MKdV equation [14], Boussinesq equation [15] and high-dimensional ZK equation [16], mZK equation [17], KP equation [18] and so on. The actual atmospheric ocean system is very complex, compared with the single equation of low dimension, the coupled equations set [19][20][21]of high dimension are more practical.…”

Section: Introductionmentioning

confidence: 99%

Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids

Chen

Yang

2019

Mathematics

View full text Add to dashboard Cite

In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved ( G ′ / G ) -expansion method.

show abstract

“…The organization of this paper is as follows: Section 2 presents the lump solutions for Eq. (1) based on Hirota's bilinear form and symbolic computation [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Section 3 discusses the interaction solutions between lump solution and the stripe soliton.…”

Section: Introductionmentioning

confidence: 99%

Stripe solitons and lump solutions for a generalized Kadomtsev–Petviashvili equation with variable coefficients in fluid mechanics

Liu

2019

Nonlinear Dyn

View full text Add to dashboard Cite

Under investigation is a generalized (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation with variable coefficients in fluid dynamics. Based on the Hirota's bilinear form and the positive quadratic function, abundant lump solutions are obtained. The interaction solutions between lump solutions and other solitons are also presented. Their dynamical behaviors are graphically shown with different choices of the free parameters.

show abstract

Dynamics of the breather waves, rogue waves and solitary waves in an extend Kadomtsev–Petviashvili equation

Cited by 15 publications

References 63 publications

Breather Wave and Traveling Wave Solutions for A (2 + 1)-Dimensional KdV4 Equation

Breather Wave and Traveling Wave Solutions for A (2 + 1)-Dimensional KdV4 Equation

Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids

Stripe solitons and lump solutions for a generalized Kadomtsev–Petviashvili equation with variable coefficients in fluid mechanics

Contact Info

Product

Resources

About