Fourier-Galerkin Method for Time Dependent Problems of Interacting Localized Waves

We develop a Fourier-Galerkin spectral technique for computing solutions of type of interacting localized waves. We use a special complete orthonormal system of functions in L2(-, ). The rate of convergence of the coefficients is shown to be exponential. As a featured example we consider the Boussinesq Paradigm Equation (BPE). We obtain results for the head-on and overtaking collisions of two or three solitons. We evaluate also the phase shifts of solitons.