scholarly journals Approximate symmetries and conservation laws in topological insulators and associated Z-invariants

2020 ◽  
Vol 419 ◽  
pp. 168238
Author(s):  
Nora Doll ◽  
Hermann Schulz-Baldes
Keyword(s):  
Conservation Laws ◽  
Topological Insulators ◽  
Approximate Symmetries

scholarly journals Approximate symmetries and similarity solutions for wave equations on liquid films

2020 ◽  
pp. 18-18
Author(s):  
Sameerah Jamal ◽  
Andronikos Paliathanasis
Keyword(s):  
Conservation Laws ◽  
Small Amplitude ◽  
Wave Equations ◽  
Liquid Films ◽  
Similarity Solutions ◽  
Lie Symmetries ◽  
Long Waves ◽  
Approximate Symmetries ◽  
Approximate Similarity ◽  
Perturbation Parameters

We study the exact and approximate Lie symmetries for two equations which describe long waves with small amplitude on liquid films. Specifically, we study the 1+2 Benney-Luke and the 1+1 Benney-Lin equations, both from an exact and approximate perspective. To induce approximate symmetries, we show that terms involving derivatives higher than two are necessarily selected as the perturbation parameters. We construct conservation laws for both equations, and illustrate how the approximate point symmetries can be used to determine approximate similarity solutions.

scholarly journals Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tahir Ayaz ◽  
Farhad Ali ◽  
Wali Khan Mashwani ◽  
Israr Ali Khan ◽  
Zabidin Salleh ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Third Order ◽  
Lagrange Method ◽  
Approximate Symmetries ◽  
Weakly Nonlinear ◽  
The Kdv Equation ◽  
De Vries ◽  
Perturbed Kdv Equation

The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system.

Particles dynamics around time conformal quintessential Schwarzschild black hole

2020 ◽  
Vol 29 (13) ◽  
pp. 2050095
Author(s):  
Israr Ali Khan ◽  
Amir Sultan Khan ◽  
Saeed Islam ◽  
Farhad Ali
Keyword(s):  
Black Hole ◽  
Small Parameter ◽  
Conservation Laws ◽  
Charged Particles ◽  
Conformal Factor ◽  
Noether Symmetries ◽  
Schwarzschild Black Hole ◽  
Approximate Symmetries ◽  
Particles Dynamics ◽  
General Time

In this paper, the effect of time is explored on the dynamics of neutral and charged particles around the Schwarzschild (Sch) black hole (BH) environed by quintessence. We introduce a general time conformal factor [Formula: see text] to the quintessential Sch spacetime, where [Formula: see text] is a time ([Formula: see text])-dependent function and [Formula: see text], a small parameter, that causes perturbation in the corresponding spacetime. The Noether symmetry equation is obtained with the help of Lagrangian corresponding to time conformal Sch spacetime environed by quintessence. Consequently, we get a 19 partial differential equations (PDEs) system. The solution of this system gives Noether symmetries, Noether approximate symmetries, and the corresponding conservation laws. The dynamics of neutral/charged particles are studied as well as graphically analyzed at the foot of these invariants.

scholarly journals Approximate Symmetry Analysis and Approximate Conservation Laws of Perturbed KdV Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yu-Shan Bai ◽  
Qi Zhang
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Symmetry Algebra ◽  
Optimal System ◽  
Approximate Symmetry ◽  
Invariant Solutions ◽  
Approximate Symmetries ◽  
One Dimensional ◽  
Perturbed Kdv Equation ◽  
Partial Lagrangian

Approximate symmetries, which are admitted by the perturbed KdV equation, are obtained. The optimal system of one-dimensional subalgebra of symmetry algebra is obtained. The approximate invariants of the presented approximate symmetries and some new approximately invariant solutions to the equation are constructed. Moreover, the conservation laws have been constructed by using partial Lagrangian method.

scholarly journals Perturbed Korteweg-de Vries equations symmetry analysis and conservation laws

2019 ◽  
Vol 23 (4) ◽  
pp. 2281-2289
Author(s):  
Yu-Shan Bai ◽  
Qi Zhang
Keyword(s):  
Conservation Laws ◽  
Coupled System ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Transformation Groups ◽  
Invariant Solutions ◽  
Approximate Symmetries ◽  
De Vries ◽  
Small Parameters ◽  
Partial Lagrangian

Approximate symmetries for a coupled system of perturbed Korteweg-de Vries equations with small parameters are constructed by applying the method of approximate transformation groups. The optimal system of the presented approximate symmetries and a few approximate invariant solutions to the coupled system are obtained. Moreover, approximate conservation laws are constructed by using the partial Lagrangian method.

scholarly journals FOURTH-ORDER PATTERN FORMING PDES: PARTIAL AND APPROXIMATE SYMMETRIES

2020 ◽  
Vol 25 (2) ◽  
pp. 198-207
Author(s):  
Sameerah Jamal ◽  
Andrew G. Johnpillai
Keyword(s):  
Conservation Laws ◽  
Fourth Order ◽  
Nonlinear Models ◽  
Approximate Solutions ◽  
Perturbation Parameter ◽  
Primary Method ◽  
Approximate Symmetries ◽  
Pattern Forming ◽  
Sivashinsky Equation ◽  
Order Pattern

This paper considers pattern forming nonlinear models arising in the study of thermal convection and continuous media. A primary method for the derivation of symmetries and conservation laws is Noether’s theorem. However, in the absence of a Lagrangian for the equations investigated, we propose the use of partial Lagrangians within the framework of calculating conservation laws. Additionally, a nonlinear Kuramoto-Sivashinsky equation is recast into an equation possessing a perturbation term. To achieve this, the knowledge of approximate transformations on the admissible coefficient parameters is required. A perturbation parameter is suitably chosen to allow for the construction of nontrivial approximate symmetries. It is demonstrated that this selection provides approximate solutions.

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