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...

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.

The main objective of this article is to analyse the dynamics of Burgers equation on the unit interval, driven by affine linear white noise. It is shown that the solution field of the stochastic Burgers equation generates a smooth perfect and locally compacting cocycle on the energy space L2([0, 1],R). Using multiplicative ergodic theory techniques, we establish the existence of a discrete non-...

In this paper, based on the known first integral method, we try to seek the traveling wave solutions of several nonlinear evolution equations. As a result, some exact travelig wave solutions and solitary solutions for Whitham-Broer-Kaup (WBK) equations, Gardner equation, Boussinesq-Burgers equations, nonlinear schrodinger equation and mKDV equation are established successfully. Key–Words: First...

In a companion paper we have solved the basic problem of full-state stabilization of unstable “shock-like” equilibrium profiles of the viscous Burgers equation with actuation at the boundaries. In this paper we consider several advanced problems for this nonlinear partial differential equation (PDE) system. We start with the problems of trajectory generation and tracking. Our algorithm is appli...

1. Determinations were made of several physical properties of the viscid and frame silks of the orb-webs built by the spider Araneus sericatus (Cl.). 2. Both types of silk show a breaking stress of approximately 1 GN/m and an initial resilience of approximately 0-35. 3. The breaking extension ratio of viscid silk (A = 3*00) is much greater than that of frame silk (A = i2s), and the viscid silk ...

The coupling of accurate computational fluid dynamics analysis with optimal control theory has the potential to advance active flow-control for complex fluid systems. In this paper, an optimal control framework for the viscous Burgers equation is constructed based on the Discontinuous Galerkin Method (DGM). A DGM discretization has several potential advantages for optimization studies including...

In a famous calculation of the “large-distance and longtime properties of a randomly stirred fluid,” Forster, Nelson, and Stephen (FNS) analyzed the consequences of various forcing scenarios for the Navier–Stokes equation and, to some extent, Burgers equation. They considered both a conservative forcing (Model A) and a nonconservative one (Model B), and predicted nontrivial properties for the l...

In this paper we construct a stochastic particle method for the Burgers equation with a monotone initial condition; we prove that the convergence rate is O(1= p N + p t) for the L 1 (IR)-norm of the error. To obtain that result, we link the PDE and the algorithm to a system of weakly interacting stochastic particles; the diiculty of the analysis comes from the discontinuity of the interaction k...