References
- L. Abia and J. Sanz-Serna. The spectral accuracy of a full-discrete scheme for a nonlinear third-order equation. Computing, 44:187–196, 1990. http://dx.doi.org/10.1007/BF02262215.
- C.T. Anh. Influence of surface tension and bottom topography on internal waves. Math. Models Methods Appl. Sci., 19(12):2145–2175, 2009. http://dx.doi.org/10.1142/S0218202509004078.
- C.T. Anh. On the Boussinesq/Full dispersion systems and Boussinesq/Boussinesq systems for internal waves. Nonlinear Anal., 72:409–429, 2010. http://dx.doi.org/10.1016/j.na.2009.06.076.
- U.M. Ascher, S.J. Ruuth and B.T.R. Wetton. Implicit–explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal., 32(3):797–823, 1995. http://dx.doi.org/10.1137/0732037.
- C. Basdevant, M. Deville, P. Haldenwang, J. Lacroix, J. Quazzani, R. Peyret, P. Orlandi and A. Patera. Spectral and finite difference solutions of the Burgers equation. Comput. Fluids, 14:23–41, 1986. http://dx.doi.org/10.1016/0045-7930(86)90036-8.
- T.B. Benjamin. Internal waves of permanent form in fluids of great depth. J. Fluid Mech., 29:559–562, 1967. http://dx.doi.org/10.1017/S002211206700103X.
- J.L. Bona, D. Lannes and J.C. Saut. Asymptotic models for internal waves. J. Math. Pures Appl., 89(9):538–566, 2008. http://dx.doi.org/10.1016/j.matpur.2008.02.003.
- W. Choi and R. Camassa. Weakly nonlinear internal waves in a two-fluids system. J. Fluid Mech., 313:83–103, 1996. http://dx.doi.org/10.1017/S0022112096002133.
- W. Choi and R. Camassa. Fully nonlinear internal waves in a two-fluid system. J. Fluid Mech., 396:1–36, 1999. http://dx.doi.org/10.1017/S0022112099005820.
- J. Garnier, R. Kraenkel and A. Nachbin. Optimal Boussinesq model for shallow-water waves interacting with a microstructure. Phys. Rev. E, 76:046311, 2007. http://dx.doi.org/10.1103/PhysRevE.76.046311.
- J.C. Muñoz Grajales. Decay of solutions of a Boussinesq-type system with variable coefficients. Waves Random Complex Media, 22(4):589–612, 2012. http://dx.doi.org/10.1080/17455030.2012.734641.
- J.C. Muñoz Grajales and A. Nachbin. Improved Boussinesq-type equations for highly-variable depths. IMA J. Appl. Math., 71:600–633, 2006. http://dx.doi.org/10.1093/imamat/hxl008.
- O. Nwogu. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterway, Port, Coastal Ocean Eng., 119(6):618–638, 1993. http://dx.doi.org/10.1061/(ASCE)0733-950X(1993)119:6(618).
- H. Ono. Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan, 39:1082–1091, 1975. http://dx.doi.org/10.1143/JPSJ.39.1082.
- J.E. Pasciak. Spectral and pseudo-spectral methods for advection equation. Math. Comput., 35:1081–1092, 1980.
- B. Pelloni and V.A. Dougalis. Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations. Appl. Numer. Math., 37:95–107, 2001. http://dx.doi.org/10.1016/S0168-9274(00)00027-1.
- A. Ruiz de Zárate and A. Nachbin. A reduced model for internal waves interacting with topography at intermediate depth. Commun. Math. Sci., 6(2):385–396, 2008. http://dx.doi.org/10.4310/CMS.2008.v6.n2.a6.
- A. Ruiz de Zárate, D.G. Alfaro Vigo, A. Nachbin and W. Choi. A higher-order internal wave model accounting for large bathymetric variations. Stud. Appl. Math., 122:275–294, 2009. http://dx.doi.org/10.1111/j.1467-9590.2009.00433.x.
- V. Tomée and A.S. Vasudeva Murphy. A numerical method for the periodic Benjamin–Ono equation. BIT, 38:597–611, 1998. http://dx.doi.org/10.1007/BF02510262.
- G.B. Whitham. Linear and Nonlinear Waves. John Wiley, New York, London, Sidney, 1974.