We study Lagrangian trajectories and scalar transport statistics in decaying Burgers turbulence. We choose velocity fields, solutions of the inviscid Burgers equation, whose probability distributions are specified by Kida’s statistics. They are time-correlated, not time-reversal invariant and not Gaussian. We discuss in some details the effect of shocks on trajectories and transport equations. ...

We study centred second-order in time and space discretizations of the inviscid Burgers equation. Although this equation in its continuum formulation supports non-smooth shock wave solutions, the discrete equation generically supports smooth solitary wave solutions. Using backward error analysis we derive the modified equation associated with the numerical scheme. We identify three different eq...

in this article we discussed the numerical solution of Burgers’ equation using multigrid method. We used implicit method for time discritization and Crank-Nicolson scheme for space discritization for fully discrete scheme. For improvement we used Multigrid method in fully discrete solution. And also Multigrid method accelerates convergence of a basics iterative method by global correction. Nume...

A 2 1 dimensional Burgers equation and a coupled higher dimensional Burgers system is studied by the singular manifold method. The Bäcklund transformations are obtained. Some interesting exact solutions are given. Then localized structures, such as dromion and solitoff, are found, and their interaction properties are numerically studied. The fusion phenomena of two dromions, a dromion and a sol...

Salas, Gomez and Heranańdez [A.Y. Salas S., C.A. Gomez S., J.E.C Hernańdez, New abundant solutions for tha Burgers equation, Computers and Mathematics with Applications 58 (2009) 514 -520] presented 70 ”new exact solutions” of a ”generalized version” of the Burgers equation. In this comment we show that all 70 solutions by these authors are not new and cannot be new. PACS: 02.30.Jr Ordinary dif...

In this article, we prove that the Kolmogorov operator associated to the Burgers equation driven by a space-time white noise is m-dissipative. This implies several properties on the Kolmogorov equation. This result is obtained thanks to the introduction of a modified Kolmogorov operator. New a priori estimates on the solutions of the Burgers equation and on the invariant measure are obtained. T...

This paper is devoted to the study of initial-boundary value problems for time-fractional analogues Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and modified Vries-Burgers equations on a bounded domain. Sufficient conditions blowing-up solutions in finite time aforementioned are presented. We also discuss maximum principle influence grad...