Related papers: Low-dimensional modelling of a generalized Burgers…
In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a H\"older space. We get the temporal regularity and…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
The (2+1)-dimensional Burgers equation has been investigated first from prospective of symmetry by localizing the nonlocal residual symmetries and then studied by a simple generalized tanh expansion method. New symmetry reduction solutions…
We construct a discrete shell-model for two-dimensional turbulence that takes into account local and nonlocal interactions between velocity modes in Fourier space. In real space, its continuous limit is described by the one-dimensional…
Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
This article concerns the dressing method for solving of multidimensional nonlinear Partial Differential Equations. In particular, we join hierarchy of matrix Burgers type equation with hierarchies of equations integrable by the Inverse…
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville…
We analyze the score field of a diffusion generative model through a Burgers-type evolution law. For VE diffusion, the heat-evolved data density implies that the score obeys viscous Burgers in one dimension and the corresponding…
The present work demonstrates the connections between the Burgers, diffusion, and Schroedinger's equations. The starting point is a formulation of the stochastic mechanics, which is modeled along the lines of the scale relativity theory.…
All Lie symmetries of the Burgers equation driven by an external random force are found. Besides the generalized Galilean transformations, this equation is also invariant under the time reparametrizations. It is shown that the Gaussian…
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…
We report on the implementation of Burgers equation as a type-II quantum computation on an NMR quantum information processor. Since the flow field evolving under the Burgers equation develops sharp features over time, this is a better test…
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…
Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap, presenting a basis of this algebra in an explicit form and…
We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension $D$. We investigate the robustness of the energy transfer mechanism and of the…
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…
We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long"…
In this paper, we aim for the theta function representation of quasi-periodic solution and related crucial quantities for a two-component generalization of Burgers equation. Our tools include the theory of algebraic curve, the meromorphic…
An unconventional approach is applied to solve the one-dimensional Burgers' equation. It is based on spline polynomial interpolations and Hopf-Cole transformation. Taylor expansion is used to approximate the exponential term in the…