On the Burgers Equation with a Stochastic Stepping-Stone Noisy Term

Aspects of the Noisy Burgers Equation

The noisy Burgers equation describing for example the growth of an interface subject to noise is one of the simplest model governing an intrinsically nonequilibrium problem. In one dimension this equation is analyzed by means of the MartinSiggia-Rose technique. In a canonical formulation the morphology and scaling behavior are accessed by a principle of least action in the weak noise limit. The...

Multidimensional Stochastic Burgers Equation

We consider multidimensional stochastic Burgers equation on the torus T and the whole space R . In both cases we show that for positive viscosity ν > 0 there exists a unique strong global solution in L for p > d. In the case of torus we also establish a uniform in ν a priori estimate and consider a limit ν ↘ 0 for potential solutions. In the case of R uniform with respect to ν a priori estimate...

Solitons in the noisy Burgers equation.

We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension. The equations support stable right hand and left hand solitons and in the low viscosity limit a long-lived soliton pair excitation. We find that two identical pai...

On the Stochastic Burgers Equation with Moving Boundary

This paper studies the stochastic Burgers equation with moving boundaries. The solution is obtained numerically by employing differentiation matrices which are derived from spectral collocation. The stochastic term is considered only to be timedependent. It is argued that the solely time-dependent stochastic term does not create considerable amount of perturbation in the wave profile between th...

On Numerical Approximation of Stochastic Burgers’ Equation