Bäcklund transformations, consistent Riccati expansion solvability, and soliton–cnoidal interaction wave solutions of Kadomtsev–Petviashvili equation

2020 ◽  
Vol 29 (2) ◽  
pp. 020201
Author(s):  
Ping Liu ◽  
Jie Cheng ◽  
Bo Ren ◽  
Jian-Rong Yang
Keyword(s):  
Bäcklund Transformations ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Backlund Transformations ◽  
Consistent Riccati Expansion

Painlevé Test, Bäcklund Transformation and Consistent Riccati Expansion Solvability for two Generalised Cylindrical Korteweg-de Vries Equations with Variable Coefficients

2018 ◽  
Vol 73 (3) ◽  
pp. 207-213 ◽  
Author(s):  
Rehab M. El-Shiekh
Keyword(s):  
Vries Equation ◽  
Dusty Plasmas ◽  
Variable Coefficients ◽  
Bäcklund Transformations ◽  
Painlevé Test ◽  
New Exact Solutions ◽  
Backlund Transformations ◽  
Integrability Conditions ◽  
De Vries ◽  
Consistent Riccati Expansion

AbstractIn this paper, the integrability of the (2+1)-dimensional cylindrical modified Korteweg-de Vries equation and the (3+1)-dimensional cylindrical Korteweg-de Vries equation with variable coefficients arising in dusty plasmas in its generalised form was studied by two different techniques: the Painlevé test and the consistent Riccati expansion solvability. The integrability conditions and Bäcklund transformations are constructed. By using Bäcklund transformations and the solutions of the Riccati equation many new exact solutions are found for the two equations in this study. Finally, the application of the obtained solutions in dusty plasmas is investigated.

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