EXPLICIT AND EXACT SOLUTIONS FOR THE NONLINEAR POISSON EQUATION

2021 ◽  
Vol 110 (1) ◽  
pp. 19-26
Author(s):  
Yuan-Xi Xie
Keyword(s):  
Exact Solutions ◽  
Poisson Equation

EXPLICIT EXACT SOLUTIONS TO THE (2+1) DIMENSIONAL SINH-POISSON EQUATION

2010 ◽  
Vol 24 (17) ◽  
pp. 3395-3409
Author(s):  
YUANXI XIE ◽  
SHIYU PENG
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Poisson Equation ◽  
Variable Separation ◽  
Simple Manner

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation, many explicit exact solutions of the (2+1) dimensional sinh-Poisson equation are presented in a simple manner.

scholarly journals Reduction of the Self-dual Yang-Mills Equations to Sinh-Poisson Equation and Exact Solutions

2021 ◽  
Vol 20 ◽  
pp. 540-546
Author(s):  
Gharib. M. Gharib ◽  
Rania Saadeh
Keyword(s):  
Exact Solutions ◽  
Poisson Equation ◽  
Negative Curvature ◽  
Travelling Wave ◽  
The Self ◽  
Travelling Wave Solution ◽  
Constant Negative Curvature ◽  
Differential Systems ◽  
Yang Mills ◽  
Spherical Surfaces

The geometric properties of differential systems are used to demonstrate how the sinh-poisson equation describes a surface with a constant negative curvature in this paper. The canonical reduction of 4-dimensional self dual Yang Mills theorem is the sinh-poisson equation, which explains pseudo spherical surfaces. We derive the B¨acklund transformations and the travelling wave solution for the sinh-poisson equation in specific. As a result, we discover exact solutions to the self-dual Yang-Mills equations.

Exact solutions of the collisional Vlasov equation

1998 ◽  
Vol 59 (1) ◽  
pp. 169-177 ◽  
Author(s):  
A. M. EL-HANBALY ◽  
A. ELGARAYHI
Keyword(s):  
Exact Solutions ◽  
Symmetry Group ◽  
Poisson Equation ◽  
Vlasov Equation ◽  
Planck Equation ◽  
Similarity Solutions ◽  
System Of Equations ◽  
The Poisson Equation ◽  
Fokker Planck Equation ◽  
Different Types

The symmetry group of the Vlasov–Fokker–Planck equation (VFPE) is constructed. The effects of the Poisson equation on this group is studied, and different types of similarity solutions of the whole system of equations (VFPE+Poisson equation) are obtained.

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