Related papers: Burgers' equation in non-commutative space-time
In this follow up paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of infinite mass initial datas. We show that an enhanced…
This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The…
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…
In this paper we are extending the well known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example we apply the theory to the case of a differential-difference…
In the first part of this paper we linearize and solve the Van der Pol and Lienard equations with some additional nonlinear terms by the application of a generalized form of Cole-Hopf transformation. We then show that the same…
In this work, a Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for d-dimensional coupled Burgers' equations is developed. We first adopt the Cole-Hopf transformation where an…
Besides its various applications in string and D-brane physics, the $\theta$-deformation of space (-time) coordinates (naively called the noncommutativity of coordinates), based on the $\star$-product, behaves as a more general framework…
The vector Burgers equation is extended to include pressure gradients and gravity. It is shown that within the framework of the Cole-Hopf transformation there are no physical solutions to this problem. This result is important because it…
In this project we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defining a process via a kind of Feynman-Kac…
In this paper we discuss the relation between non-homogeneous nonlinear fractional diffusive equations and the Schrodinger equation with time-dependent harmonic potential. It is well known that the Cole-Hopf transformation allows to…
Exactly solvable variable parametric Burgers type equations in one-dimension are introduced, and two different approaches for solving the corresponding initial value problems are given. The first one is using the relationship between the…
We emphasize that construction of travelling wave solutions for partial differential equations is a problem of considerable interest and thus introduce a simple algebraic method to generate such solutions for equations in the Burgers…
We consider a nonhomogeneous Burgers equation with time variable coefficients, and obtain an explicit solution of the general initial value problem in terms of solution to a corresponding linear ODE. Special exact solutions such as…
The Burgers' equation is a one-dimensional momentum equation for a Newtonian fluid. The Cole-Hopf transformation solves the equation for a given initial and boundary condition. However, in most cases the resulting integral equation can only…
In this paper, we obtained the non-local residual symmetry related to truncated Painlev\'e expansion of Burgers equation. In order to localize the residual symmetry, we introduced new variables to prolong the original Burgers equation into…
In this paper, the initial value problem of the convection-diffusion equation of Burgers type is treated. In the asymptotic profile of solutions, the nonlinearity of the equation is reflected. Regarding the solutions to this model, the…
The noiseless Burgers equation in one spatial dimension is analyzed from the point of view of a diffusive evolution equation in terms of nonlinear soliton modes and linear diffusive modes. The transient evolution of the profile is…
We consider invariant measures for the stochastic Burgers equation on $\mathbb{R}$, forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth in space. An invariant measure is indecomposable, or…
In this paper, we investigate the symmetry properties of a variable coefficient nonlinear space-time fractional Burgers' equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the…
A hierarchy of normalized classes of generalized Burgers equations is studied. The equivalence groupoids of these classes are computed. The equivalence groupoids of classes of linearizable generalized Burgers equations are related to those…