Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion

1968 ◽  
Vol 9 (8) ◽  
pp. 1204-1209 ◽  
Author(s):  
Robert M. Miura ◽  
Clifford S. Gardner ◽  
Martin D. Kruskal
Keyword(s):  
Conservation Laws ◽  
Vries Equation ◽  
De Vries ◽  
Constants Of Motion

Ablowitz–Kaup–Newell–Segur system, conservation laws and Bäcklund transformation of a variable-coefficient Korteweg–de Vries equation in plasma physics, fluid dynamics or atmospheric science

2020 ◽  
Vol 34 (25) ◽  
pp. 2050226 ◽  
Author(s):  
Yu-Qi Chen ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
He Li ◽  
Xue-Hui Zhao ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Atmospheric Science ◽  
Backlund Transformation ◽  
Atmospheric Flow ◽  
Bilinear Bäcklund Transformation ◽  
De Vries ◽  
Nonlinearity Dispersion

For a variable-coefficient Korteweg–de Vries equation in a lake/sea, two-layer liquid, atmospheric flow, cylindrical plasma or interactionless plasma, in this paper, we derive the bilinear Bäcklund transformation, non-isospectral Ablowitz–Kaup–Newell–Segur system and infinite conservation laws for the wave amplitude under certain constraints among the external force, dissipation, nonlinearity, dispersion and perturbation.

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