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

  • M. A. Christou
  • C. I. Christov


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.

Spectral methods Galerkin approximation cubic Boussinesq equation localized solutions solitons 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • M. A. Christou
    • 1
  • C. I. Christov
    • 1
  1. 1.Department of MathematicsUniversity of Louisiana at LafayetteLafayette

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