Fourier-Galerkin Method for Localized Solutions of Equations with Cubic Nonlinearity

M. A. Christou, C. I. Christov

Research output: Contribution to journalArticle

14 Citations (Scopus)


Using a complete orthonormal system of functions in L2(-∞, ∞) a Fourier-Galerkin spectral technique is developed for computing of the localized solutions of equations with cubic nonlinearity. A formula expressing the triple product into series in the system is derived. Iterative algorithm implementing the spectral method is developed and tested on the soliton problem for the cubic Boussinesq equation. Solution is obtained and shown to compare quantitatively very well to the known analytical one. The issues of convergence rate and truncation error are discussed.

Original languageEnglish
Pages (from-to)63-77
Number of pages15
JournalJournal of Computational Analysis and Applications
Issue number1
Publication statusPublished - 2002


  • Cubic Boussinesq equation
  • Galerkin approximation
  • Localized solutions
  • Solitons
  • Spectral methods

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