scholarly journals Invariant Solutions and Conservation Laws of the (2 + 1)-Dimensional Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Wenjuan Rui ◽  
Peiyi Zhao ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Boussinesq Equation ◽  
Lie Symmetry ◽  
Invariant Solutions ◽  
Symmetry Approach ◽  
Lie Symmetry Approach ◽  
Conservation Theorem ◽  
Lagrange Approach

Invariant solutions and conservation laws of the (2 + 1)-dimensional Boussinesq equation are studied. The Lie symmetry approach is used to obtain the invariant solutions. Conservation laws for the underlying equation are derived by utilizing the new conservation theorem and the partial Lagrange approach.

Symmetry analysis with similarity reduction, new exact solitary wave solutions and conservation laws of (3 + 1)-dimensional extended quantum Zakharov–Kuznetsov equation in quantum physics

2021 ◽  
pp. 2150163
Author(s):  
Vinita ◽  
S. Saha Ray
Keyword(s):  
Conservation Laws ◽  
Quantum Physics ◽  
Physical Structure ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Similarity Reduction ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach ◽  
Conservation Theorem

A recently defined (3+1)-dimensional extended quantum Zakharov–Kuznetsov (QZK) equation is examined here by using the Lie symmetry approach. The Lie symmetry analysis has been used to obtain the varieties in invariant solutions of the extended Zakharov–Kuznetsov equation. Due to existence of arbitrary functions and constants, these solutions provide a rich physical structure. In this paper, the Lie point symmetries, geometric vector field, commutative table, symmetry groups of Lie algebra have been derived by using the Lie symmetry approach. The simplest equation method has been presented for obtaining the exact solution of some reduced transform equations. Finally, by invoking the new conservation theorem developed by Nail H. Ibragimov, the conservation laws of QZK equation have been derived.

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 Symmetries, Traveling Wave Solutions, and Conservation Laws of a(3+1)-Dimensional Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Letlhogonolo Daddy Moleleki ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Traveling Wave ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Lie Symmetry Method ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Symmetry Method ◽  
Conservation Theorem

We analyze the(3+1)-dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the(3+1)-dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the(3+1)-dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.

scholarly journals Solutions and Conservation Laws of a (2+1)-Dimensional Boussinesq Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Letlhogonolo Daddy Moleleki ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Boussinesq Equation ◽  
Nonlinear Evolution ◽  
Lie Symmetry ◽  
Lie Symmetry Method ◽  
Simplest Equation Method ◽  
Evolution Partial Differential Equation ◽  
First Time ◽  
Symmetry Method ◽  
Conservation Theorem

We study a nonlinear evolution partial differential equation, namely, the (2+1)-dimensional Boussinesq equation. For the first time Lie symmetry method together with simplest equation method is used to find the exact solutions of the (2+1)-dimensional Boussinesq equation. Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1)-dimensional Boussinesq equation.

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.

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