S. Liao and Y. Tan, “A General Approach to Obtain Series Solutions of Nonlinear Differential Equations,” Studies in Applied Mathematics, Vol. 119, No. 4, 2007, pp. 297-354.

has been cited by the following article:

• 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.