scholarly journals Lie symmetry and non-Noether conserved quantities of variable mass Birkhoffian system

2006 ◽  
Vol 55 (8) ◽  
pp. 3813
Author(s):  
Zhang Peng-Yu ◽  
Fang Jian-Hui
Keyword(s):  
Variable Mass ◽  
Lie Symmetry ◽  
Conserved Quantities ◽  
Birkhoffian System

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.

The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass

2008 ◽  
Vol 17 (3) ◽  
pp. 754-758 ◽  
Author(s):  
Shi Shen-Yang ◽  
Fu Jing-Li ◽  
Huang Xiao-Hong ◽  
Chen Li-Qun ◽  
Zhang Xiao-Bo
Keyword(s):  
Variable Mass ◽  
Mechanical Systems ◽  
Lie Symmetries ◽  
Conserved Quantities ◽  
Discrete Mechanical Systems

scholarly journals Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1012
Author(s):  
Innocent Simbanefayi ◽  
Chaudry Masood Khalique
Keyword(s):  
Real World ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Lie Symmetry ◽  
Conserved Quantities ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Higher Dimensional ◽  
Petviashvili Equation ◽  
Group Invariant Solutions

In this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and logarithmic solutions. The solutions derived in this paper are the most general since they contain elliptic functions. Finally, we derive the conserved quantities of this equation by employing two approaches—the general multiplier approach and Ibragimov’s theorem. The importance of conservation laws is explained in the introduction. It should be pointed out that the investigation of higher dimensional nonlinear partial differential equations is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.

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