Entire solution originating from three fronts for a discrete diffusive equation

New Entire Positive Solution for the Nonlinear Schrödinger Equation: Coexistence of Fronts and Bumps

In this paper we construct a new kind of positive solutions of ∆u− u + u = 0 on R when p > 2. These solutions have the following asymptotic behavior u(x, z) ∼ ω(x− f(z)) + ∞ ∑ i=1 ω0((x, z)− ξi~e1) as L → +∞ where ω is a unique positive homoclinic solution of ω′′−ω+ωp = 0 in R ; ω0 is the two dimensional positive solution and ~e1 = (1, 0) and ξj are points such that ξj = jL + O(1) for all j ≥ 1...

A Functional Equation Originating from Elliptic Curves

Diffusive behavior from a quantum master equation

We study a general class of translation invariant quantum Markov evolutions for a particle on Z. We assume locality of the spatial jumps and exponentially fast relaxation in momentum space. It is shown that the particle position diffuses in the long time limit. We employ a fiber decomposition in momentum space of the evolution made possible by the translation invariance of the dynamics. A centr...

General Solution of the Three-site Master Equation and the Discrete Riccati Equation

We first obtain by analogy with the continuous (differential) case the general solution of the discrete Riccati equation. Moreover, we establish the full equivalence between our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. Our results can be considered the discrete analog of Mielnik's construction in supersymmetric quantum mechanics [J. Math. ...

Perturbation Solution to the Convection-Diffusion Equation with Moving Fronts

Electrophoresis of a solute through a column in which its transport is governed by the convection diffusion equation is described. Approximate solutions to the convection difision equation in the limit of small diffusion are developed using perturbation methods. The difision coeficient and velocity are assumed to be functions of space and time such that both undergo a sudden change from one con...