Abstract
We develop a robust Christov-Galerkin spectral technique for computing interacting localized wave solutions of and fourth and sixth-order generalized wave equations. To this end, a special complete orthonormal system of functions in L2(-∞,∞) is used whose rate of convergence is shown to be exponential for the cases under consideration. For the time-stepping, an implicit algorithm is chosen which makes use of the banded structure of the matrices representing the different spatial derivatives. As featuring examples, the head-on collision of solitary waves is investigated for a sixth-order generalized Boussinesq equation and a fourth-order Boussinesq type equation with a linear term. Its solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). The numerical results are validated against published data in the literature using the method of variational imbedding.
Original language | English |
---|---|
Pages (from-to) | 245-257 |
Number of pages | 13 |
Journal | Applied Mathematics and Computation |
Volume | 243 |
DOIs | |
Publication status | Published - 15 Sept 2014 |
Keywords
- Boussinesq equations
- Kawahara solitons
- Soliton interaction
- Spectral methods