We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schrödinger boundary data problem for the random matter transport. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In g...

Considering the fractal structure of space-time, a Burgers – Korteweg – de Vries (BKdV) type equation is obtained. Particularly, if the motions of the “non-differentiable fluid” are irrotational, the BKdV type equation is reduced to a non-linear Schrödinger type equation. In this case, the scalar complex velocity field simultaneously becomes wave function.

We consider the Langevin equation describing a non-viscous Burgers fluid stochastically perturbed by uniform noise. We introduce a deterministic function that corresponds to the mean of the velocity when we keep fixed the value of the position. We study interrelations between this function and the solution of the non-perturbed Burgers equation. Especially we are interested in the property of th...

We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with degenerate equilibrium arising after traveling transformation are investigated. By finding certain positive definite Lyapunov functions neighborhood singular points and Hopf bifurcation points, number possible limit cycles corresponding is determined. existence equation...

The paper is concerned with a numerical simulation of Burgers flow as a simplified model of unsteady flow of a compressible viscous fluid. Viscous Burgers equation represents many of the properties of unsteady compressible NavierStokes equations, such as nonlinear convection and viscous diffusion leading to shock waves and boundary layers. A one-dimensional Burgers equation is frequently used t...