Multiple-front solutions for the Burgers equation and the coupled Burgers equations

2007 ◽  
Vol 190 (2) ◽  
pp. 1198-1206 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Burgers Equation ◽  
Burgers Equations ◽  
Front Solutions

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

Soliton solutions of Burgers equations and perturbed Burgers equation

2010 ◽  
Vol 216 (11) ◽  
pp. 3370-3377 ◽  
Author(s):  
Anwar Ja’afar Mohamad Jawad ◽  
Marko D. Petković ◽  
Anjan Biswas
Keyword(s):  
Burgers Equation ◽  
Soliton Solutions ◽  
Burgers Equations

Classification and Recursion Operators of Dark Burgers’ Equation

2018 ◽  
Vol 73 (2) ◽  
pp. 175-180 ◽  
Author(s):  
Mei-Dan Chen ◽  
Biao Li
Keyword(s):  
Symbolic Computation ◽  
Free Parameter ◽  
Burgers Equation ◽  
Differential Polynomial ◽  
Higher Order ◽  
Recursion Operators ◽  
Burgers Equations ◽  
Dual Symmetry ◽  
Free Parameters

AbstractWith the help of symbolic computation, two types of complete scalar classification for dark Burgers’ equations are derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark Burgers’ systems; so some special equations including symmetry equation and dual symmetry equation are obtained by selecting the free parameter. Furthermore, two kinds of recursion operators for these dark Burgers’ equations are constructed by two direct assumption methods.

scholarly journals Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2326
Author(s):  
Noufe H. Aljahdaly ◽  
Ravi P. Agarwal ◽  
Rasool Shah ◽  
Thongchai Botmart
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Singular Kernel ◽  
Exact Results ◽  
Burgers Equations ◽  
Kernel Operators ◽  
Natural Decomposition

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results.

scholarly journals Numerical approximation of coupled 1D and 2D non-linear Burgers’ equations by employing Modified Quartic Hyperbolic B-spline Differential Quadrature Method

2021 ◽  
Vol 15 ◽  
pp. 37-55
Author(s):  
Mamta Kapoor ◽  
Varun Joshi
Keyword(s):  
Present Method ◽  
Numerical Approximation ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Differential Quadrature Method ◽  
Quadrature Method ◽  
B Spline ◽  
Numerical Examples ◽  
Burgers Equations ◽  
Weighting Coefficients

In this paper, the numerical solution of coupled 1D and coupled 2D Burgers' equation is provided with the appropriate initial and boundary conditions, by implementing "modified quartic Hyperbolic B-spline DQM". In present method, the required weighting coefficients are computed using modified quartic Hyperbolic B-spline as a basis function. These coupled 1D and coupled 2D Burgers' equations got transformed into the set of ordinary differential equations, tackled by SSPRK43 scheme. Efficiency of the scheme and exactness of the obtained numerical solutions is declared with the aid of 8 numerical examples. Numerical results obtained by modified quartic Hyperbolic B-spline are efficient and it is easy to implement

scholarly journals B-spline collocation methods for numerical solutions of the Burgers' equation

2005 ◽  
Vol 2005 (5) ◽  
pp. 521-538 ◽  
Author(s):  
Idris Dag ◽  
Dursun Irk ◽  
Ali Sahin
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Collocation Methods ◽  
Test Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method ◽  
Burgers Equations

Both time- and space-splitted Burgers' equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers' equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers' equation. The results of both schemes are compared for some test problems.

scholarly journals OCCURRENCE AND NON-APPEARANCE OF SHOCKS IN FRACTAL BURGERS EQUATIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 479-499 ◽  
Author(s):  
NATHAËL ALIBAUD ◽  
JÉRÔME DRONIOU ◽  
JULIEN VOVELLE
Keyword(s):  
Initial Data ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Fractional Power ◽  
Initial Condition ◽  
Small Initial Data ◽  
Lipschitz Continuous ◽  
Burgers Equations ◽  
Smooth Initial Data ◽  
The Creation

We consider the fractal Burgers equation (that is to say the Burgers equation to which is added a fractional power of the Laplacian) and we prove that, if the power of the Laplacian involved is lower than 1/2, then the equation does not regularize the initial condition: on the contrary to what happens if the power of the Laplacian is greater than 1/2, discontinuities in the initial data can persist in the solution and shocks can develop even for smooth initial data. We also prove that the creation of shocks can occur only for sufficiently "large" initial conditions, by giving a result which states that, for smooth "small" initial data, the solution remains at least Lipschitz continuous.

scholarly journals Iterative and Noniterative Splitting Methods of the Stochastic Burgers’ Equation: Theory and Application

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1243
Author(s):  
Jürgen Geiser
Keyword(s):  
Numerical Analysis ◽  
Numerical Experiments ◽  
Burgers Equation ◽  
Splitting Methods ◽  
Iterative Schemes ◽  
Burgers Equations ◽  
Stochastic Burgers Equation ◽  
Strang Splitting ◽  
Numerical Approaches

In this paper, we discuss iterative and noniterative splitting methods, in theory and application, to solve stochastic Burgers’ equations in an inviscid form. We present the noniterative splitting methods, which are given as Lie–Trotter and Strang-splitting methods, and we then extend them to deterministic–stochastic splitting approaches. We also discuss the iterative splitting methods, which are based on Picard’s iterative schemes in deterministic–stochastic versions. The numerical approaches are discussed with respect to decomping deterministic and stochastic behaviours, and we describe the underlying numerical analysis. We present numerical experiments based on the nonlinearity of Burgers’ equation, and we show the benefits of the iterative splitting approaches as efficient and accurate solver methods.

scholarly journals Equivalence Conditions and Invariants for the General Form of Burgers’ Equations

2021 ◽  
Author(s):  
Mostafa Hesamiarshad
Keyword(s):  
Differential Equations ◽  
Burgers Equation ◽  
Equivalence Problem ◽  
Independent Variables ◽  
Burgers Equations ◽  
Structure Equations ◽  
Equivalence Of Differential Equations ◽  
Local Equivalence ◽  
Two Independent Variables ◽  
Contact Transformations

AbstractEquivalence of differential equations is one of the most important concepts in the theory of differential equations. In this paper, the moving coframe method is applied to solve the local equivalence problem for the general form of Burgers’ equation, which has two independent variables under action of a pseudo-group of contact transformations. Using this method, we found the structure equations and invariants of these equations, as a result some conditions for equivalence of them will be given.

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