scholarly journals Solitons and Bäcklund transformation for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

2016 ◽  
Vol 60 ◽  
pp. 96-100 ◽  
Author(s):  
Zhong-Zhou Lan ◽  
Yi-Tian Gao ◽  
Jin-Wei Yang ◽  
Chuan-Qi Su ◽  
Chen Zhao ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Petviashvili Equation ◽  
Dimensional Variable

Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

2018 ◽  
Vol 32 (02) ◽  
pp. 1750170 ◽  
Author(s):  
Zi-Jian Xiao ◽  
Bo Tian ◽  
Yan Sun
Keyword(s):  
Fluid Dynamics ◽  
Shock Waves ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Bilinear Forms ◽  
Backlund Transformation ◽  
Bell Polynomial ◽  
Soliton Interactions ◽  
Petviashvili Equation ◽  
Dimensional Variable

In this paper, we investigate a (2[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of [Formula: see text] and [Formula: see text] can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where [Formula: see text] and [Formula: see text] are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

Truncated Painlevé Expansion with Symbolic Computation for a General Kadomtsev-Petviashvili Equation with Variable Coefficients

1996 ◽  
Vol 51 (3) ◽  
pp. 175-178
Author(s):  
Bo Tian ◽  
Yi-Tian Gao
Keyword(s):  
Symbolic Computation ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Variable Coefficients ◽  
Explicit Solutions ◽  
Current Interest ◽  
Backlund Transformation ◽  
Petviashvili Equation ◽  
Mathematical Sciences ◽  
Truncated Painlevé Expansion

Able to realistically model various physical situations, the variable-coefficient generalizations of the celebrated Kadmotsev-Petviashvili equation are of current interest in physical and mathematical sciences. In this paper, we make use of both the truncated Painleve expansion and symbolic computation to obtain an auto-Bäcklund transformation and certain soliton-typed explicit solutions for a general Kadomtsev-Petviashvili equation with variable coefficients.

Incompressible-Fluid Symbolic Computation and Bäcklund Transformation: (3+1)-Dimensional Variable-Coefficient Boiti–Leon–Manna–Pempinelli Model

2015 ◽  
Vol 70 (1) ◽  
pp. 59-61 ◽  
Author(s):  
Xin-Yi Gao
Keyword(s):  
Shock Wave ◽  
Incompressible Fluid ◽  
Symbolic Computation ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Incompressible Fluids ◽  
Current Interest ◽  
Backlund Transformation ◽  
Wave Type ◽  
Dimensional Variable

AbstractIncompressible fluids are of current interest. Considering a (3+1)-dimensional variable-coefficient Boiti–Leon–Manna–Pempinelli model for an incompressible fluid, we perform symbolic computation to work out a variable-coefficient-dependent auto-Bäcklund transformation, along with two variable-coefficient-dependent classes of the shock-wave-type solutions. Our auto-Bäcklund transformation is different from the recently reported bilinear one.

BÄCKLUND TRANSFORMATION AND ANALYTIC SOLUTIONS FOR A GENERALIZED VARIABLE-COEFFICIENT MODIFIED KORTEWEG–DE VRIES MODEL FROM FLUID DYNAMICS AND PLASMAS

2008 ◽  
Vol 19 (11) ◽  
pp. 1659-1671 ◽  
Author(s):  
FU-WEI SUN ◽  
YI-TIAN GAO ◽  
CHUN-YI ZHANG ◽  
XIAO-GE XU
Keyword(s):  
Fluid Dynamics ◽  
External Force ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Backlund Transformation ◽  
De Vries

We investigate a generalized variable-coefficient modified Korteweg–de Vries model with perturbed factor and external force (vc-GmKdV) describing fluid dynamics and space plasmas. In this paper, we propose an extended variable-coefficient balancing-act method (Evc-BAM), which is concise and straightforward, to obtain the generalized analytic solutions including solitary wave solution of the vc-GmKdV model with symbolic computation. Meanwhile, using the Evc-BAM, we obtain an auto-Bäcklund transformation for the vc-GmKdV model on the relevant constraint conditions of the coefficient functions. Using the given auto-Bäcklund transformation, the solutions of special equations for the vc-GmKdV model are also obtained as the variable-coefficient Korteweg–de Vries (vc-KdV) equation, the generalized KdV equation with perturbed factor and external force (GKdV), the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation, and the variable-coefficient cylindrical modified Korteweg–de Vries (vc-cmKdV) equation, respectively.

Bäcklund Transformation and Soliton Solutions for a (3+1)-Dimensional Variable-Coefficient Breaking Soliton Equation

2016 ◽  
Vol 71 (9) ◽  
pp. 797-805 ◽  
Author(s):  
Chen Zhao ◽  
Yi-Tian Gao ◽  
Zhong-Zhou Lan ◽  
Jin-Wei Yang
Keyword(s):  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Bell Polynomials ◽  
Propagation Characteristics ◽  
Backlund Transformation ◽  
Soliton Equation ◽  
Dimensional Variable ◽  
Interaction Behaviors

AbstractIn this article, a (3+1)-dimensional variable-coefficient breaking soliton equation is investigated. Based on the Bell polynomials and symbolic computation, the bilinear forms and Bäcklund transformation for the equation are derived. One-, two-, and three-soliton solutions are obtained via the Hirota method.N-soliton solutions are also constructed. Propagation characteristics and interaction behaviors of the solitons are discussed graphically: (i) solitonic direction and position depend on the sign of the wave numbers; (ii) shapes of the multisoliton interactions in the scaled space and time coordinates are affected by the variable coefficients; (iii) multisoliton interactions are elastic for that the velocity and amplitude of each soliton remain unchanged after each interaction except for a phase shift.

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