Christov-Galerkin Expansion for Localized Solutions in Model Equations with Higher Order Dispersion

摘要

We develop a Galerkin spectral technique for computing localized solutions of equations with higher order dispersion. To this end, the complete orthonormal system of functions in L2(?,) proposed by Christov [1] is used.As a featuring example, the Sixth-Order Generalized Boussinesq Equation (6GBE) is investigated whose solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). Localized solutions are obtained here numerically for the case of the moving frame which are used as initial conditions for the time dependent problem.