In this paper, a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term -k2x + f(t), k is an element of R is presented. Two methods existing for the case K=0 are adapted and generalized using variable and functional transformations, valid for all values of space and time. The emergence of a Fokker-Planck equation in the method allows the establishme...

The Burgers’ equation is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers’ equation using the finite difference and collocation methods. With the temporal discretization of the equation using C-N scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical results of two d...

Burgers’ equations is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers’ equation numerically using the finite difference and collocation methods. After the temporal discretization of the equation using C-N Scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical result...

Richard J. A. M. Stevens, Herman J. H. Clercx, and Detlef Lohse Department of Science and Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands and Department of Physics and J. M. Burgers Centre for Fluid Dynamics, Eindh...

A comparative study of non-coplanar binary dislocation junctions in magnesium (Mg) and beryllium (Be) is presented to examine the effects of elastic properties and active Burgers vectors on junction formation and destruction in hexagonal close-packed (hcp) crystals via discrete dislocation dynamics simulations. Two junction configurations formed at intersecting prismatic ð01 10Þ=basal ð0001Þ pl...

We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report...

We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the gaussian unitary ensemble, on which we focus in this paper, we show that the characteristics polynomials and their inverse evolve according to a...