References
- Boussinesq J. Théorie des ondes et des remous qui se propagent le long d’un canal rectangularie horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement parailles de la surface au found. J Math Pures Appl. 1872;17:55–108.
- Korteweg DJ, Vries G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos Mag. 1985;39:422–443.
- Boussinesq J. Théorie générale des mouvements qui sont propagés dans un canal rectangularie horizontal. C R Acad Sci. 1871;73:256–260.
- Bona JL, Smith R. A model for the two-way propagation of water waves in a channel. Math Proc Cambridge Phil Soc. 1976;79:167–182.
- Bona JL, Chen M, Saut JC. Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: derivation and linear theory. J Nonlinear Sci. 2002;12(4):283–318.
- Bona JL, Chen M, Saut JC. Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory. Nonlinearity. 2004;17(3):925–952.
- Antonopoulos DC, Dougalis VA. Notes on error estimates for Galerkin approximations of the classical Boussinesq system and related hyperbolic problems. Preprint, 2010.
- Antonopoulos DC, Dougalis VA. Numerical solution of the “classical” Boussinesq system. Math Comput Simul. 2010;82(6):984–1007.
- Antonopoulos DC, Dougalis VA. Error estimates for Galerkin approximations of the classical Boussinesq system. Math Comput. 2013;82(282):689–717.
- Antonopoulos DC, Dougalis VA, Mitsotakis DE. Numerical solution of Boussinesq systems of the Bona-Smith family. Appl Numer Math. 2010;60:314–336.
- Bona JL, Dougalis VA, Mitsotakis DE. Numerical solution of KdV-KdV systems of Boussinesq equations: I. The numerical scheme and generalized solitary waves. Math Comput Simul. 2007;74(2–3):214–228.
- Dougalis VA, Mitsotakis DE, Saut JC. Boussinesq systems of Bona-Smith type on plane domains: theory and numerical analysis. J Sci Comput. 2010;44(2):109–135.
- Rincon MA, Xavier JC, Alfaro Vigo DG. Analysis and computation of a nonlinear Korteweg-de Vries system. BIT Numer Math. 2016;(56):1069–1099.
- Iorio R, Iorio V. Fourier analysis and partial differential equations. Cambridge: Cambridge University Press; 2001.
- Trefethen LN. Spectral methods in Matlab. Society for Industrial and Applied Mathematics. Oxford: Oxford University; 2000.
- Canuto C, Hussaini MY, Quarteroni A, et al. Spectral methods. Fundamentals in single domains. Berlin: Springer; 2006.
- Ascher U. Numerical methods for evolutionary differential equations. Philadelphia (PA): SIAM; 2008.
- Alfaro Vigo DG, Oliveira SP, de Zárate AR, et al. Fully discrete stability and dispersion analysis for a linear dispersive internal wave model. Comput Appl Math. 2014;33:203–221.
- Hesthaven JS, Gottlieb S, Gottlieb D. Spectral methods for time-dependent problems. Cambridge: Cambridge University Press; 2007.
- Chen H, Chen M, Nguyen NV. Cnoidal wave solutions to Boussinesq systems. Nonlinearity. 2007;20:1443–1461.
- Antonopoulos DC, Dougalis VA, Mitsotakis DE. Galerkin approximations of periodic solutions of Boussinesq systems. Bull Greek Math Soc. 2010;57:13–30.
- Chen M. Exact traveling-wave solutions to bidirectional wave equations. Int J Theor Phys. 1998;37:1547–1567.
- Hairer E, Nørsett S, Wanner G. Solving ordinary differential equations I. Berlin: Springer; 2008.
- Pelloni B, Dougalis VA. Numerical modeling of two way propagation of nonlinear dispersive waves. Math Comput Simul. 2001;55:595–606.