scholarly journals Motions of Curves in the Pseudo-Galilean SpaceG31

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Suleyman Cengiz ◽  
Esra Betul Koc Ozturk ◽  
Ufuk Ozturk
Keyword(s):  
Burgers Equations ◽  
Frenet Equations

We study the flows of curves in the pseudo-Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motions of curves in the pseudo-Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers’ equations.

Motions of Curves in 4-Dimensional Galilean Space G4

2021 ◽  
pp. 2150153
Author(s):  
Hülya Gün Bozok ◽  
Sezin Aykurt Sepet ◽  
Mahmut Ergüt
Keyword(s):  
Vector Fields ◽  
Invariant Vector ◽  
Burgers Equations ◽  
Frenet Equations ◽  
Inextensible Flows ◽  
Galilean Space ◽  
Invariant Vector Fields

In this paper, we investigate the flow of curve and its equiform geometry in 4-dimensional Galilean space. We obtain that the Frenet equations and curvatures of inextensible flows of curves and its equiformly invariant vector fields and intrinsic quantities are independent of time. We find that the motions of curves and its equiform geometry can be defined by the inviscid and stochastic Burgers’ equations in 4-dimensional Galilean space.

scholarly journals On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin
Keyword(s):  
Periodic Boundary ◽  
Asymptotic Formulas ◽  
Burgers Equations ◽  
Spherical Waves ◽  
Constant Height ◽  
De Vries ◽  
Spatial Dimensions ◽  
Integral Characteristics ◽  
Boundary Solutions ◽  
Shock Fronts

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

scholarly journals Recursion operators admitted by non-Abelian Burgers equations: Some remarks

2018 ◽  
Vol 147 ◽  
pp. 40-51 ◽  
Author(s):  
Sandra Carillo ◽  
Mauro Lo Schiavo ◽  
Cornelia Schiebold
Keyword(s):  
Recursion Operators ◽  
Burgers Equations

Generalized Burgers Equations Transformable to the Burgers Equation

2011 ◽  
Vol 127 (3) ◽  
pp. 211-220 ◽  
Author(s):  
B. Mayil Vaganan ◽  
T. Jeyalakshmi
Keyword(s):  
Burgers Equation ◽  
Burgers Equations

scholarly journals Stochastic heat and Burgers equations and their singularities. I. Geometrical properties

2002 ◽  
Vol 43 (6) ◽  
pp. 3293-3328 ◽  
Author(s):  
Ian M Davies ◽  
Aubrey Truman ◽  
Huaizhong Zhao
Keyword(s):  
Geometrical Properties ◽  
Burgers Equations
Sign in / Sign up

Export Citation Format

Share Document