TITLE:
A Series Solution for the Ginzburg-Landau Equation with a Time-Periodic Coefficient
AUTHORS:
Pradeep G. Siddheshwar
KEYWORDS:
Ginzburg-Landau Equation, Modulation, Nonlinear Convection
JOURNAL NAME:
Applied Mathematics,
Vol.1 No.6,
December
27,
2010
ABSTRACT: The solution of the real Ginzburg-Landau (GL) equation with a time-periodic coefficient is obtained in the form of a series, with assured convergence, using the computer-assisted ‘Homotopy Analysis Method’ (HAM) propounded by Liao [1]. The formulation has been kept quite general to keep open the possibility of obtaining the solution of the GL equation for different continua as limiting cases of the present study. New ideas have been added and clear explanations are provided in the paper to the existing concepts in HAM. The method can easily be extended to solve complex GL equation, system of GL equations or even the GL equations with a diffusion term, each having a time-periodic coefficient. The necessary code in Mathematica that implements the HAM for the current problem is appended to the paper for use by the readers.