Binary Darboux transformation for a variable-coefficient nonisospectral modified Kadomtsev–Petviashvili equation with symbolic computation

2015 ◽  
Vol 83 (3) ◽  
pp. 1463-1468 ◽  
Author(s):  
Juan Li ◽  
Xing-Fa Gu ◽  
Tao Yu ◽  
Yu-Lin Zhan ◽  
Zhi Liu ◽  
...  
Keyword(s):  
Symbolic Computation ◽  
Darboux Transformation ◽  
Variable Coefficient ◽  
Petviashvili Equation ◽  
Binary Darboux Transformation

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.

scholarly journals Lump and Lump-Type Solutions of the Generalized (3+1)-Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Yanni Zhang ◽  
Jing Pang
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Variable Coefficient ◽  
Three Dimensional ◽  
Petviashvili Equation ◽  
Hirota Bilinear Form ◽  
Contour Plots ◽  
Dimensional Variable ◽  
Hirota Bilinear

Based on the Hirota bilinear form of the generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation, the lump and lump-type solutions are generated through symbolic computation, whose analyticity can be easily achieved by taking special choices of the involved parameters. The property of solutions is investigated and exhibited vividly by three-dimensional plots and contour plots.

Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

2008 ◽  
Vol 49 (4) ◽  
pp. 833-838 ◽  
Author(s):  
Zhang Ya-Xing ◽  
Zhang Hai-Qiang ◽  
Li Juan ◽  
Xu Tao ◽  
Zhang Chun-Yi ◽  
...  
Keyword(s):  
Symbolic Computation ◽  
Darboux Transformation ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Lax Pair ◽  
De Vries ◽  
Fifth Order
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