Lie symmetry reductions and group invariant solutions of (2 + 1)-dimensional modified Veronese web equation

2019 ◽  
Vol 98 (3) ◽  
pp. 1891-1903 ◽  
Author(s):  
Sachin Kumar ◽  
Amit Kumar
Keyword(s):  
Lie Symmetry ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Symmetry Reductions ◽  
Group Invariant Solutions

Group Invariant Solutions and Conservation Laws of the Fornberg– Whitham Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 489-496 ◽  
Author(s):  
Mir Sajjad Hashemi ◽  
Ali Haji-Badali ◽  
Parisa Vafadar
Keyword(s):  
Exact Solutions ◽  
Reduction Method ◽  
Lie Symmetry ◽  
First Integrals ◽  
Invariant Solutions ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Whitham Equation

In this paper, we utilize the Lie symmetry analysis method to calculate new solutions for the Fornberg-Whitham equation (FWE). Applying a reduction method introduced by M. C. Nucci, exact solutions and first integrals of reduced ordinary differential equations (ODEs) are considered. Nonlinear self-adjointness of the FWE is proved and conserved vectors are computed

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.

scholarly journals Some General New Einstein Walker Manifolds

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mehdi Nadjafikhah ◽  
Mehdi Jafari
Keyword(s):  
Partial Differential Equations ◽  
Symmetry Group ◽  
Lie Symmetry ◽  
Group Method ◽  
Invariant Solutions ◽  
Point Symmetry Group ◽  
One Dimensional ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Walker Manifold

Lie symmetry group method is applied to find the Lie point symmetry group of a system of partial differential equations that determines general form of four-dimensional Einstein Walker manifold. Also we will construct the optimal system of one-dimensional Lie subalgebras and investigate some of its group invariant solutions.

Stochastic Bifurcations of Group-Invariant Solutions for a Generalized Stochastic Zakharov–Kuznetsov Equation

2021 ◽  
Vol 31 (03) ◽  
pp. 2150040
Author(s):  
Changzhao Li ◽  
Hui Fang
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Lie Symmetry ◽  
Nonlinear Wave Equations ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Bifurcation Phenomena ◽  
Group Invariant Solutions ◽  
Stochastic Ordinary Differential Equations ◽  
Stochastic Bifurcations

In this paper, we introduce the concept of stochastic bifurcations of group-invariant solutions for stochastic nonlinear wave equations. The essence of this concept is to display bifurcation phenomena by investigating stochastic P-bifurcation and stochastic D-bifurcation of stochastic ordinary differential equations derived by Lie symmetry reductions of stochastic nonlinear wave equations. Stochastic bifurcations of group-invariant solutions can be considered as an indirect display of bifurcation phenomena of stochastic nonlinear wave equations. As a constructive example, we study stochastic bifurcations of group-invariant solutions for a generalized stochastic Zakharov–Kuznetsov equation.

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