Related papers: Fisher Equation for a Decaying Brane
We study an inhomogeneous decay of an unstable D-brane in the context of Dirac-Born-Infeld~(DBI)-type effective action. We consider tachyon and electromagnetic fields with dependence of time and one spatial coordinate, and an exact solution…
Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly…
The dynamics (in light-cone time) of the tachyon on an unstable brane in the background of a dilaton linear along a null coordinate is a non-local reaction-diffusion type equation, which admits a travelling front solution. We analyze the…
Nonlinear non-stationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus instability, is derived. The new equation respects all the conservation laws to be…
We propose an alternative interpretation of the boundary state for the rolling tachyon, which may depict the time evolution of unstable D-branes in string theory. Splitting the string variable in the temporal direction into the classical…
Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized…
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…
The decay of an unstable D-brane via closed string emission and open string pair production is considered in subcritical string theory with a spacelike linear dilaton. The decay rate is given by the imaginary part of the annulus, which has…
We present an exact time-dependent solution to the effective D-brane world-volume theory which describes an inhomogeneous decay of a brane-antibrane system. We compute the quantum energy flux induced by the particle creation in this…
The goal of this paper is to describe the metastable dynamics of the solutions to the reaction-diffusion equation with nonlinear phase-dependent diffusion $u_t=\varepsilon^2(D(u)u_x)_x-f(u)$, where $D$ is a strictly positive function and…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…
A quantum kinetic equation is obtained for an inhomogeneous solid having arbitrary gradient concentration and chemical potential. We find, starting from nonequilibrium statistical operator, a new equation to describe atom migration in solid…
We investigate the spatially inhomogeneous decay of an unstable D-brane and construct an asymptotic solution which describes a codimension one D-brane and the tachyon matter in boundary string field theory. In this solution, the tachyon…
In this paper closed string emission and open string pair production from the light-like rolling tachyon solution are calculated in subcritical string theory in the background of a linear dilaton. The rolling light-like tachyon represents…
We explore the effects of non-abelian dynamics of D-branes on their stability and introduce Hitchin-like modifications to previously-known stability conditions. The relation to brane-antibrane systems is used in order to rewrite the…
We prove sharp estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations on a bounded domain subject to a homogeneous Dirichlet boundary condition. Important special cases are the…
Recently, Hellerman and Schnabl considered the dynamics of unstable D-branes in the background of a linear dilaton. Remarkably, they were able to construct light-like tachyon solutions which interpolate smoothly between the perturbative and…
We discuss how to describe time-dependent phenomena in string theory like the decay of unstable D-branes with the help of the world-sheet formulation. It is shown in a nontrivial well-controlled example that the coupling of the tachyons to…
Unstable D-branes are central objects in string theory, and exist also in time-dependent backgrounds. In this paper we take first steps to studying brane decay in spacetime orbifolds. As a concrete model we focus on the R^{1,d}/Z_2…
Fisher waves have been studied recently in the specific case of diffusion-limited reversible coalescence, A+A<-->A, on the line. An exact analysis of the particles concentration showed that waves propagate from a stable region to an…