We study the kinetics of two-species annihilation, A + B → 0, when all particles undergo strictly biased motion in the same direction and with an excluded volume repulsion between same species particles. It was recently shown that the density in this system decays as t −1/3 , compared to t −1/4 density decay in A+B → 0 with isotropic diffusion and either with or without the hard-core repulsion....

Spatially coarse-grained (or effective) versions of nonlinear partial differential equations must be closed with a model for the unresolved small scales. For systems that are known to display fractal scaling, we propose a model based on synthetically generating a scale-invariant field at small scales using fractal interpolation, and then analytically evaluating its effects on the large, resolve...

Abstract In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|e 2/2, β ≥ 0, x ∈ R. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted ge...

We establish a simple relation between certain curvatures of the group of volumepreserving diffeomorphisms and the lifespan of potential solutions to the inviscid Burgers equation before the appearance of shocks. We show that shock formation corresponds to a focal point of the group of volume-preserving diffeomorphisms regarded as a submanifold of the full diffeomorphism group and, consequently...

In this study, we applied the generalized Kudryashov method to two different conformable fractional differential equations and one system namely Burgers’ equation with derivative, Wu-Zhang sinh-Gordon equation. Obtained solutions are soliton-type solutions. All obtained have been verified considered correct by placing them in original help of Maple software program. Also, plotted three-dimensio...