New classes of exact solutions to the Grad-Shafranov equation with arbitrary flow using Lie-point symmetries

2016 ◽  
Vol 23 (11) ◽  
pp. 112508 ◽  
Author(s):  
Ap. Kuiroukidis ◽  
G. N. Throumoulopoulos
Keyword(s):  
Exact Solutions ◽  
Lie Point Symmetries ◽  
Shafranov Equation ◽  
Arbitrary Flow

Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation

2019 ◽  
Vol 16 (02) ◽  
pp. 1950032 ◽  
Author(s):  
Azadeh Naderifard ◽  
S. Reza Hejazi ◽  
Elham Dastranj ◽  
Ahmad Motamednezhad
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Vector Fields ◽  
Kdv Equation ◽  
Group Analysis ◽  
Invariant Subspaces ◽  
Similarity Solutions ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Symmetry Operators

In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity solutions of the equation are presented by using the obtained optimal system. Finally, a useful method called invariant subspaces is applied in order to find another solutions.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

scholarly journals On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Sait San ◽  
Emrullah Yaşar
Keyword(s):  
Liquid Crystals ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Nematic Liquid Crystals ◽  
Lie Point Symmetries ◽  
Local Conservation ◽  
The Relationship ◽  
Conservation Method

We study the modified Hunter-Saxton equation which arises in modelling of nematic liquid crystals. We obtain local conservation laws using the nonlocal conservation method and multiplier approach. In addition, using the relationship between conservation laws and Lie-point symmetries, some reductions and exact solutions are obtained.

Conservation Laws and Exact Solutions with Symmetry Reduction of Nonlinear Reaction Diffusion Equations

2015 ◽  
Vol 16 (3-4) ◽  
pp. 191-196 ◽  
Author(s):  
Filiz Tascan ◽  
Arzu Yakut
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Lie Point Symmetries ◽  
Important Place ◽  
Physical Problems ◽  
Nonlinear Reaction

AbstractIn this work we study one of the most important applications of symmetries to physical problems, namely the construction of conservation laws. Conservation laws have important place for applications of differential equations and solutions, also in all physics applications. And so, this study deals conservation laws of first- and second-type nonlinear (NL) reaction diffusion equations. We used Ibragimov’s approach for finding conservation laws for these equations. And then, we found exact solutions of first- and second-type NL reaction diffusion equations with Lie-point symmetries.

scholarly journals Lie Symmetry Analysis and Exact Solutions of Generalized Fractional Zakharov-Kuznetsov Equations

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 601 ◽  
Author(s):  
Changzhao Li ◽  
Juan Zhang
Keyword(s):  
Exact Solutions ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
New Exact Solutions ◽  
Symmetry Properties

This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation. Accordingly, we study the vector fields of this equation. Meantime, the symmetry reductions of this equation are performed. Finally, by employing the obtained symmetry properties, we can get some new exact solutions to this fractional Zakharov-Kuznetsov equation.

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