scholarly journals Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients

Symmetry ◽  
2018 ◽  
Vol 10 (2) ◽  
pp. 41
Author(s):  
Vasyl’ Davydovych
Keyword(s):  
Lie Symmetry ◽  
Time Dependent ◽  
Volterra System

Direct approach to a group classification problem: Fisher equation with time-dependent coefficients

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640021
Author(s):  
Motlatsi Molati ◽  
Chaudry Masood Khalique
Keyword(s):  
Reaction Diffusion ◽  
Classification Problem ◽  
Lie Symmetry ◽  
Group Classification ◽  
Time Dependent ◽  
Model Parameters ◽  
Fisher Equation ◽  
Lie Symmetry Analysis ◽  
Physical Systems ◽  
Diffusion Convection

We perform Lie symmetry analysis of a time-variable coefficient Fisher equation which models reaction–diffusion–convection phenomena in biological, chemical and physical systems. These time-dependent coefficients (model parameters or arbitrary elements) are specified via the direct integration of the classifying relations.

scholarly journals Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2434
Author(s):  
Ruixin Li ◽  
Lianzhong Li
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Time Dependent ◽  
Series Solutions ◽  
Lie Symmetry Analysis ◽  
Gardner Equation ◽  
Power Series Solutions ◽  
Conservation Theorem

In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the symmetry reduction of the equation, and then the power series solutions in some specific cases are obtained. By virtue of the fractional conservation theorem, the conservation laws are constructed.

EXPLICITLY SPACE- AND TIME-DEPENDENT D'ALEMBERT EQUATIONS WITH SYMMETRIES

1999 ◽  
Vol 14 (26) ◽  
pp. 4189-4200
Author(s):  
MARIANNA EULER ◽  
NORBERT EULER ◽  
OVE LINDBLOM
Keyword(s):  
Lorentz Symmetry ◽  
Lie Symmetry ◽  
Time Dependent ◽  
Two Dimensional ◽  
Symmetry Generator ◽  
Symmetry Reductions ◽  
Space And Time ◽  
D’Alembert Equation ◽  
Symmetry Algebras

The general d'Alembert equation □u + f (x0, x1, u) = 0 is considered, where □ is the two-dimensional d'Alembert operator. We classify the equation for functions f by which it admits several Lie symmetry algebras, which include the Lorentz symmetry generator. The corresponding symmetry reductions are listed.

Introduction and permanence of species in a diffusive Lotka-Volterra system with time-dependent coefficients

2005 ◽  
Vol 183 (1) ◽  
pp. 1-9 ◽  
Author(s):  
J.F. López-Sánchez ◽  
F. Alhama ◽  
C.F. González-Fernández
Keyword(s):  
Time Dependent ◽  
Volterra System
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