Related papers: A sequence approach to solve the Burgers' equation
In this paper we present a simple and accurate second order finite element scheme to simulate the Burgers' equation on the whole real line and subjected to initial conditions with compact support. The numerical simulations are performed by…
We study a formulation of Burgers equation on the Sierpinski gasket, which is the prototype of a p.c.f. self-similar fractal. One possibility is to implement Burgers equation as a semilinear heat equation associated with the Laplacian for…
Burgers' equation with fixed Dirichlet boundary conditions is considered on generic bounded intervals. By using the Hopf-Cole transformation and the exact operational solution recently established for linear reaction-diffusion equations…
After reviewing the source-type solution of the Burgers equation with standard dissipativity, we study the hypoviscous counterpart of the Burgers equation. 1) We determine an equation that governs the near-identity transformation underlying…
This paper represents a mixed numerical method for the multi-resolution solution of non-linear partial differential equations based on B-Spline wavelets. The method is based on a second-order finite difference formula combined with the…
Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the…
In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.
In this paper, the new (2+1)-dimensional Burgers equation has been derived using the Burgers equation' recursion operator as follows \begin{equation*} u_{xt}+\left(u_{t}+uu_{x}-\nu…
A detailed analysis of the invariant point transformations for the first four partial differential equations which belong to the Complex Burgers` Hierarchy is performed. Moreover, a detailed application of the reduction process through the…
In this short letter we show that the one dimensional non linear Schr\"odinger equation(NLS)can be solved by a Hopf-Cole transformation which converts it to the Burgers equation in turbulence.
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
We prove that the stochastic Burgers equation, which is related to the Kardar-Parisi-Zhang/KPZ equation via weak derivative, is a "critical" scaling limit for density fluctuations for a family of non-integrable and non-stationary…
In this paper, we establish the existence and uniqueness of solutions to the two-dimensional Burgers equation using the framework of infinite-dimensional dynamical systems. The two-dimensional Burgers equation, which models the interplay…
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…
A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences…
We consider Burgers equation with transverse viscosity $$\partial_tu+u\partial_xu-\partial_{yy}u=0, \ \ (x,y)\in \mathbb R^2, \ \ u:[0,T)\times \mathbb R^2\rightarrow \mathbb R.$$ We construct and describe precisely a family of solutions…
When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets…
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…
Admissible point transformations between Burgers equations with linear damping and time-dependent coefficients are described and used in order to exhaustively classify Lie symmetries of these equations. Optimal systems of one- and…
The Moyal *-deformed noncommutative version of Burgers' equation is considered. Using the *-analog of the Cole-Hopf transformation, the linearization of the model in terms of the linear heat equation is found. Noncommutative q-deformations…