Variational Derivative

2020 ◽  
pp. 2600-2600
Keyword(s):  
Variational Derivative

scholarly journals Conservation Laws for a Degasperis Procesi Equation and a Coupled Variable-Coefficient Modified Korteweg-de Vries System in a Two-Layer Fluid Model via the Multiplier Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
E. Osman ◽  
M. Khalfallah ◽  
H. Sapoor
Keyword(s):  
Conservation Laws ◽  
Variable Coefficient ◽  
Fluid Model ◽  
Variational Derivative ◽  
Derivative Method ◽  
De Vries

We employ the multiplier approach (variational derivative method) to derive the conservation laws for the Degasperis Procesi equation and a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Firstly, the multipliers are computed and then conserved vectors are obtained for each multiplier.

STABILITY OR METASTABILITY AND EIGENVALUES OF THE EQUATION OF SMALL FLUCTUATIONS

1990 ◽  
Vol 05 (07) ◽  
pp. 1319-1339 ◽  
Author(s):  
H.J.W. MÜLLER-KIRSTEN ◽  
ZHANG JIAN-ZU ◽  
D.H. TCHRAKIAN
Keyword(s):  
Negative Eigenvalue ◽  
Variational Derivative ◽  
Euclidean Action ◽  
Double Well Potential

A theory with an asymmetric double-well potential is discussed and shown to possess a nontopological classical configuration like a bounce. It is then shown that the second variational derivative of the Euclidean action at this bounce-like configuration does not possess a negative eigenvalue. The significance of this observation is discussed in relation to more familiar models. Then a theory with a cubic potential is discussed and shown to possess a bounce with one negative eigenvalue of the second variational derivative which is indicative of metastability.

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