Peakon numerical solution of Cammasa-Holm non-linear equation
Amir Hossein Parand1, Seyed Reza Mousavi2, Samira Safajoo3
In this paper peakon solitary waves solution of Cammasa-Holm non- linear equation obtained by numerical methods and peaked soliton solution are investigated by examining these waves interaction. The Cammassa- Holm is a non-linear third order equation because its peakon solutions has a discontinuity of derivative at its wave peak and cannot be solved using conventional numerical methods .Finite difference and Spectral methods are used to solve this equation .In finite difference method we used separated forms and upstream and downstream trick. In spectral Fourier method (by Fourier transformation), non-linear equation transform from physical space to Fourier space and in this new space becomes linear and can solve by one of common numerical methods. Eventually by inverse Fourier transformation, solutions transforms to physical space to observed. Soliton , peakon and anti peakon solutions of Cammasa- Holm equation can be illustrated as well by spectral method.