scholarly journals Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1277
Author(s):  
María S. Bruzón ◽  
Tamara M. Garrido ◽  
Elena Recio ◽  
Rafael de la Rosa
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Formulation ◽  
Soliton Solutions ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
Point Of View ◽  
Variational Structure ◽  
Potential Form ◽  
Line Soliton ◽  
Low Order

In this work, we study a generalised (2+1) equation of the Zakharov–Kuznetsov (ZK)(m,n,k) equation involving three arbitrary functions. From the point of view of the Lie symmetry theory, we have derived all Lie symmetries of this equation depending on the arbitrary functions. Line soliton solutions have also been obtained. Moreover, we study the low-order conservation laws by applying the multiplier method. This family of equations is rich in Lie symmetries and conservation laws. Finally, when the equation is expressed in potential form, it admits a variational structure in the case when two of the arbitrary functions are linear. In addition, the corresponding Hamiltonian formulation is presented.

scholarly journals New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1001 ◽  
Author(s):  
Subhadarshan Sahoo ◽  
Santanu Saha Ray ◽  
Mohamed Aly Mohamed Abdou ◽  
Mustafa Inc ◽  
Yu-Ming Chu
Keyword(s):  
Conservation Laws ◽  
Fractional Differential Equations ◽  
Soliton Solutions ◽  
Logistic Function ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Fractional Differential ◽  
Physical Phenomena

New soliton solutions of fractional Jaulent-Miodek (JM) system are presented via symmetry analysis and fractional logistic function methods. Fractional Lie symmetry analysis is unified with symmetry analysis method. Conservation laws of the system are used to obtain new conserved vectors. Numerical simulations of the JM equations and efficiency of the methods are presented. These solutions might be imperative and significant for the explanation of some practical physical phenomena. The results show that present methods are powerful, competitive, reliable, and easy to implement for the nonlinear fractional differential equations.

Soliton Solutions, Conservation Laws, and Reductions of Certain Classes of NonlinearWave Equations

2012 ◽  
Vol 67 (10-11) ◽  
pp. 613-620 ◽  
Author(s):  
Richard Morris ◽  
Abdul Hamid Kar ◽  
Abhinandan Chowdhury ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Lie Symmetry ◽  
Nonlinear Wave Equations ◽  
Conserved Quantities ◽  
Symmetry Approach ◽  
Lie Symmetry Approach

In this paper, the soliton solutions and the corresponding conservation laws of a few nonlinear wave equations will be obtained. The Hunter-Saxton equation, the improved Korteweg-de Vries equation, and other such equations will be considered. The Lie symmetry approach will be utilized to extract the conserved densities of these equations. The soliton solutions will be used to obtain the conserved quantities of these equations.

scholarly journals Conservation laws and line soliton solutions of a family of modified KP equations

2020 ◽  
Vol 13 (10) ◽  
pp. 2655-2665 ◽  
Author(s):  
Stephen C. Anco ◽  
◽  
Maria Luz Gandarias ◽  
Elena Recio ◽  
Keyword(s):  
Conservation Laws ◽  
Soliton Solutions ◽  
Kp Equations ◽  
Line Soliton

Lie Symmetries for Discrete Electromechanical Dynamical Systems with Irregular Lattices

2011 ◽  
Vol 138-139 ◽  
pp. 267-272
Author(s):  
Gang Ling Zhao ◽  
Li Qun Chen ◽  
Jing Li Fu
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Maxwell Equation ◽  
Structural Equations ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
Discrete Variables ◽  
Generalized Coordinates ◽  
Continuous And Discrete Variables ◽  
Infinitesimal Transformations

In this article, we study Lie symmetries and conservation laws of the discrete electromechanical dynamical systems with irregular lattices. The Lagrange-Maxwell equation and transformation operators in the space of continuous and discrete variables are introduced, the determining equations and the structural equations of Lie symmetry theory are obtained under infinitesimal transformations with respect to generalized coordinates. Finally, we discuss an example to illustrate these results.

Exact Group Invariant Solutions and Conservation Laws of the Complex Modified Korteweg–de Vries Equation

2013 ◽  
Vol 68 (8-9) ◽  
pp. 510-514 ◽  
Author(s):  
Andrew G. Johnpillai ◽  
Abdul H. Kara ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Symmetry Algebra ◽  
Lie Symmetry ◽  
Point Of View ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Symmetry Approach ◽  
De Vries ◽  
Group Invariant Solutions ◽  
Symmetry Generators

We study the scalar complex modified Korteweg-de Vries (cmKdV) equation by analyzing a system of partial differential equations (PDEs) from the Lie symmetry point of view. These systems of PDEs are obtained by decomposing the underlying cmKdV equation into real and imaginary components. We derive the Lie point symmetry generators of the system of PDEs and classify them to get the optimal system of one-dimensional subalgebras of the Lie symmetry algebra of the system of PDEs. These subalgebras are then used to construct a number of symmetry reductions and exact group invariant solutions to the system of PDEs. Finally, using the Lie symmetry approach, a couple of new conservation laws are constructed. Subsequently, respective conserved quantities from their respective conserved densities are computed.

scholarly journals Lie symmetry reductions and conservation laws for fractional order coupled KdV system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Hong Guang Sun ◽  
Marzieh Azadi
Keyword(s):  
Conservation Laws ◽  
Fractional Order ◽  
Lie Symmetry ◽  
Theoretical Physics ◽  
Lie Symmetry Analysis ◽  
Kdv Equations ◽  
Ode System ◽  
Coupled Kdv Equations ◽  
Scientific Phenomena ◽  
New System

AbstractLie symmetry analysis is achieved on a new system of coupled KdV equations with fractional order, which arise in the analysis of several problems in theoretical physics and numerous scientific phenomena. We determine the reduced fractional ODE system corresponding to the governing factional PDE system.In addition, we develop the conservation laws for the system of fractional order coupled KdV equations.

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