scholarly journals Differential invariants and group classification of variable coefficient generalized Gardner equation

2009 ◽  
Vol 58 (10) ◽  
pp. 6686
Author(s):  
Guo Mei-Yu ◽  
Gao Jie
Keyword(s):  
Variable Coefficient ◽  
Group Classification ◽  
Differential Invariants ◽  
Gardner Equation ◽  
Generalized Gardner Equation

Group Classification of Variable Coefficient $K\MakeLowercase{(m,n)}$ Equations

2014 ◽  
Author(s):  
Kyriakos Charalambous ◽  
Olena Vaneeva ◽  
Christodoulos Sophocleous
Keyword(s):  
Variable Coefficient ◽  
Group Classification

scholarly journals Group Classification of Variable Coefficient K(m,n) Equations

2014 ◽  
Author(s):  
Kyriakos Charalambous ◽  
Olena Vaneeva ◽  
Christodoulos Sophocleous
Keyword(s):  
Variable Coefficient ◽  
Group Classification

scholarly journals Lie Group Classification of Generalized Variable Coefficient Korteweg-de Vries Equation with Dual Power-Law Nonlinearities with Linear Damping and Dispersion in Quantum Field Theory

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 83
Author(s):  
Oke Davies Adeyemo ◽  
Chaudry Masood Khalique
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Lie Group ◽  
Variable Coefficient ◽  
Variable Coefficients ◽  
Group Classification ◽  
Quantum Field ◽  
Lie Group Classification

Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear conditions involve variable coefficients. In consequence, this article presents a complete Lie group analysis of a generalized variable coefficient damped wave equation in quantum field theory with time-dependent coefficients having dual power-law nonlinearities. Lie group classification of two distinct cases of the equation was performed to obtain its kernel algebra. Thereafter, symmetry reductions and invariant solutions of the equation were obtained. We also investigate various soliton solutions and their dynamical wave behaviours. Further, each class of general solutions found is invoked to construct conserved quantities for the equation with damping term via direct technique and homotopy formula. In addition, Noether’s theorem is engaged to furnish more conserved currents of the equation under some classifications.

scholarly journals Group classification of variable coefficient quasilinear reaction-diffusion equations

2013 ◽  
Vol 94 (108) ◽  
pp. 81-90 ◽  
Author(s):  
Olena Vaneeva ◽  
Alexander Zhalij
Keyword(s):  
Variable Coefficient ◽  
Reaction Diffusion ◽  
Group Classification ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Equivalence Group ◽  
Point Transformations

The group classification of variable coefficient quasilinear reaction diffusion equations ut = uxx + h(x)B(u) is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the study of admissible point transformations within the class.

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