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Acta Mathematica Scientia, 1986
The Burgers equation is generalized to a (compound) higher order Burger equation which can be reduced to a higher order linear equation in terms of the Bäcklund transformation (BT) between them. Also BT of the higher order Burgers equation to itself is derived.
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The Burgers equation is generalized to a (compound) higher order Burger equation which can be reduced to a higher order linear equation in terms of the Bäcklund transformation (BT) between them. Also BT of the higher order Burgers equation to itself is derived.
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Stochastically Forced Burgers Equation
1994One of the first attempts to arrive at the statistical theory of turbulent fluid motion was the proposal by Burgers of his celebrated equation, which in one space dimension is $$ {\partial _t}{u_t}(x) = v\partial _x^2{u_t}(x) - {u_t}(x){\partial _x}{u_t}(x) $$ (1) where u t (x) is the velocity field and v is the viscosity.
Bertini L +2 more
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Numerical solution of Burger's equation
Communications in Numerical Methods in Engineering, 1993AbstractIn the present paper numerical solutions of the one‐dimensional Burger equation are obtained. The technique of finitely reproducing non‐linearities introduced by Bazley is used. This technique when applied to Burger's equation gives a method where a system of non‐linear ordinary differential equations is to be solved.
Mittal, R. C., Singhal, Poonam
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On a nonhomogeneous Burgers’ equation
Science in China Series A: Mathematics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Xiaqi, Jiu, Quansen, He, Cheng
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Solution of Forced Burgers Equation
The Physics of Fluids, 1972Burgers' model equation of turbulence is studied for the case when the driving force is periodic. Analytical solution is obtained for the inviscid flow and numerical integration is performed for the viscous flow.
Jeng, D. T., Meecham, W. C.
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Inverse cascade via Burgers equation
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2000Burgers equation is employed as a pedagogical device for analytically demonstrating the emergence of a form of inverse cascade to the lowest wavenumber in a flow. The transition from highly nonlinear mode–mode coupling to an ordered preference for large scale structure is shown, both analytically (revealing the presence of a global attractor) and via a
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Optimal Prediction of Burgers’s Equation
Multiscale Modeling & Simulation, 2007Summary: We examine an application of the optimal prediction framework to the truncated Fourier-Galerkin approximation of the Burgers equation. Under particular conditions on the density of the modes and the length of the memory kernel, optimal prediction introduces an additional term to the Fourier-Galerkin approximation which represents the influence
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Remarks on the Burgers Equation
Journal of Mathematical Physics, 1968Periodic and aperiodic solutions of the Burgers equation ut + uux = μuxx, μ > 0, are studied in this paper. A harmonic analysis of the solutions is carried out and the form of the spectrum is estimated for large time. Corresponding estimates of energy decay are also made.
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2000
The Burgers equation is a simple equation to understand the main properties of the Navier-Stokes equations. In this one-dimensional equation the pressure is neglected but the effects of the nonlinear and viscous terms remain, hence as in the Navier-Stokes equations a Reynolds number can be defined.
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The Burgers equation is a simple equation to understand the main properties of the Navier-Stokes equations. In this one-dimensional equation the pressure is neglected but the effects of the nonlinear and viscous terms remain, hence as in the Navier-Stokes equations a Reynolds number can be defined.
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Diffusion equation coupled to Burgers' equation
Fluid Dynamics Research, 1987Scalar diffusion in one-dimensional Burgers' flow is considered. When the Prandtl number is unity, the diffusion equation with convective term is reduced to a simple diffusion equation by a generalized Cole-Hopf transformation. An exact solution of an initial value problem is obtained in a closed form.
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