Studying nonlinear effects on the early stage of phase ordering using a decomposition method

TL;DR

This paper investigates the early nonlinear effects in phase ordering dynamics using Adomian's decomposition method applied to the Ginzburg-Landau equation, providing analytical insights into short-time nonlinear behavior.

Contribution

It introduces a systematic polynomial expansion approach to analyze short-time nonlinear effects in phase ordering, enhancing understanding beyond linear theory.

Findings

Accurately captures short-time nonlinear dynamics

Provides analytical series solutions for the Ginzburg-Landau equation

Clarifies the onset of nonlinearities at different length scales

Abstract

Nonlinear effects on the early stage of phase ordering are studied using Adomian's decomposition method for the Ginzburg-Landau equation for a nonconserved order parameter. While the long-time regime and the linear behavior at short times of the theory are well understood, the onset of nonlinearities at short times and the breaking of the linear theory at different length scales are less understood. In the Adomian's decomposition method, the solution is systematically calculated in the form of a polynomial expansion for the order parameter, with a time dependence given as a series expansion. The method is very accurate for short times, which allows to incorporate the short-time dynamics of the nonlinear terms in a analytical and controllable way.