scholarly journals Lie symmetries of generalized Kawahara equations

2020 ◽  
pp. 3-10
Author(s):  
O.O. Vaneeva ◽  
◽  
A.Yu. Zhalij ◽  
Keyword(s):  
Variable Coefficients ◽  
Lie Symmetry ◽  
Group Classification ◽  
Lie Symmetries

We carry out the group classification of a normalized class of generalized Kawahara equations with variable coefficients. Admissible transformations are studied, and the partition of the class into two normalized subclasses is performed. For each of these subclasses, the respective equivalence groupoids are found. As a result, all equations from the class admitting Lie symmetry extensions are revealed.

scholarly journals A hunter-gatherer–farmer population model: Lie symmetries, exact solutions and their interpretation

2018 ◽  
Vol 30 (2) ◽  
pp. 338-357 ◽  
Author(s):  
R. M. CHERNIHA ◽  
V. V. DAVYDOVYCH
Keyword(s):  
Exact Solutions ◽  
Population Model ◽  
Reaction Diffusion ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
System Modelling ◽  
Hunter Gatherers ◽  
Three Component Reaction ◽  
Biological Interpretation

The Lie symmetry classification of the known three-component reaction–diffusion system modelling the spread of an initially localized population of farmers into a region occupied by hunter-gatherers is derived. The Lie symmetries obtained for reducing the system in question to systems of ordinary differential equations (ODEs) and constructing exact solutions are applied. Several exact solutions of travelling front type are also found, their properties are identified and biological interpretation is discussed.

scholarly journals Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Motlatsi Molati ◽  
Chaudry Masood Khalique
Keyword(s):  
Quadratic Forms ◽  
Type System ◽  
Lie Symmetry ◽  
Two Dimensions ◽  
Group Classification ◽  
Classical Approach ◽  
Physical Sciences ◽  
Lie Group Classification ◽  
Physical Phenomena

The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.

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 Lie Symmetry Analysis of the Time Fractional Generalized KdV Equations with Variable Coefficients

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1281 ◽  
Author(s):  
Cheng Chen ◽  
Yao-Lin Jiang ◽  
Xiao-Tian Wang
Keyword(s):  
Variable Coefficients ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Boundary Values ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Kdv Equations ◽  
Fractional Differential Operator ◽  
Generalized Kdv Equations

The group classification of a class of time fractional generalized KdV equations with variable coefficient is presented. The Lie symmetry analysis method is extended to the certain subclasses of time fractional generalized KdV equations with initial and boundary values. Under the corresponding similarity transformation with similarity invariants, KdV equations with initial and boundary values have been transformed into fractional ordinary differential equations with initial value. Then we use the power series method to obtain the exact solution of the reduced equation with the Erdélyi-Kober fractional differential operator.

Lie group classification of the N-th-order nonlinear evolution equations

2011 ◽  
Vol 54 (12) ◽  
pp. 2553-2572 ◽  
Author(s):  
ShouFeng Shen ◽  
ChangZheng Qu ◽  
Qing Huang ◽  
YongYang Jin
Keyword(s):  
Lie Group ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Group Classification ◽  
Nonlinear Evolution Equations ◽  
Lie Group Classification
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