Conservation laws for a nonlinear evolution equation that includes as a special case the cylindrical KdV equation

1978 ◽  
Vol 23 (4) ◽  
pp. 155-160 ◽  
Author(s):  
F. Calogero ◽  
A. Degaspeeis
Keyword(s):  
Evolution Equation ◽  
Conservation Laws ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Special Case

Traveling wave solutions and conservation laws of a generalized Kudryashov–Sinelshchikov equation

2019 ◽  
Vol 25 (2) ◽  
pp. 211-217 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Abdullahi Rashid Adem ◽  
Sivenathi Oscar Mbusi
Keyword(s):  
Heat Transfer ◽  
Evolution Equation ◽  
Conservation Laws ◽  
Traveling Wave ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Pressure Waves ◽  
Wave Solutions ◽  
Kudryashov Method

Abstract Kudryashov and Sinelshchikov proposed a nonlinear evolution equation that models the pressure waves in a mixture of liquid and gas bubbles by taking into account the viscosity of the liquid and the heat transfer. Conservation laws and exact solutions are computed for this underlying equation. In the analysis of this particular equation, two approaches are employed, namely, the multiplier method and Kudryashov method.

scholarly journals Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xifang Cao
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
The Other ◽  
Bäcklund Transformations ◽  
Backlund Transformations ◽  
The Kdv Equation ◽  
New Equation

We first give a Bäcklund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Bäcklund transformations with two pseudopotentials, one of which is from the KdV equation to the new equation and the other from the new equation to itself. As applications, by applying our Bäcklund transformations to known solutions, we construct some novel solutions to the new equation.

scholarly journals Soliton Solutions and Conservation Laws of a (3+1)-Dimensional Nonlinear Evolution Equation

2019 ◽  
Vol 135 (3) ◽  
pp. 539-545
Author(s):  
M. Ekici ◽  
A. Sonmezoglu ◽  
A. Rashid Adem ◽  
Qin Zhou ◽  
Zitong Luan ◽  
...  
Keyword(s):  
Evolution Equation ◽  
Conservation Laws ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions

scholarly journals Soliton solutions, Painleve analysis and conservation laws for a nonlinear evolution equation

2021 ◽  
Vol 23 ◽  
pp. 103999
Author(s):  
S.T.R. Rizvi ◽  
Aly R. Seadawy ◽  
Muhammad Younis ◽  
Ijaz Ali ◽  
S. Althobaiti ◽  
...  
Keyword(s):  
Evolution Equation ◽  
Conservation Laws ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Painlevé Analysis ◽  
Painleve Analysis

Lie symmetries and conservation laws for a generalized (2+1)-dimensional nonlinear evolution equation

2020 ◽  
Vol 58 (4) ◽  
pp. 775-798 ◽  
Author(s):  
S. Sáez ◽  
R. de la Rosa ◽  
E. Recio ◽  
T. M. Garrido ◽  
M. S. Bruzón
Keyword(s):  
Evolution Equation ◽  
Conservation Laws ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Lie Symmetries
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