Application of the Lie symmetry approach to an extended Jimbo–Miwa equation in (3+1) dimensions

2021 ◽  
Vol 136 (8) ◽  
Author(s):  
Sachin Kumar ◽  
Vishakha Jadaun ◽  
Wen-Xiu Ma
Keyword(s):  
Lie Symmetry ◽  
Symmetry Approach ◽  
Lie Symmetry Approach

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 On Hydrogen Entanglements and Gravitation: a Lie Symmetry Approach

2021 ◽  
Vol 15 ◽  
pp. 31-37
Author(s):  
JM Manale
Keyword(s):  
Gravitational Constant ◽  
Superposition Principle ◽  
Lie Symmetry ◽  
Quantum Superposition ◽  
One Dimensional ◽  
Symmetry Approach ◽  
Subatomic Particles ◽  
Popular View ◽  
The One ◽  
Lie Symmetry Approach

We depart from the popular view on how gravitation is generated. Ours is entanglement based. For an atom, hydrogen in this case, all subatomic particles, within and outside the nuclei, participate in this eternal dance. To test the idea, we use it to determine a formula for G, the universal gravitational constant. In the process, we note that the one-dimensional Schrodinger equation is not solved, as claimed. For example, existing solutions are silent on the quantum superposition principle. This we address through our modified symmetry group theoretical methods.

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