References
- Bao , W. Z. , Jin , S. and Markowich , P. A. 2002 . On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime . J. Comput. Phys. , 175 : 487 – 524 .
- Bona , J. L. , Chen , M. and Saut , J. C. 2002 . Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: derivation and linear theory . J. Nonlin. Sci. , 12 : 283 – 318 .
- Chen , M. 1998 . Exact solutions of various Boussinesq systems . Appl. Math. Lett. , 11 : 45 – 49 .
- Chen , J. B. 2005 . Multisymplectic geometry, local conservation laws and Fourier pseudospectral discretization for the “good” Boussinesq equation . Appl. Math. Comput. , 161 : 55 – 67 .
- El-Zoheiry , H. 2003 . Numerical investigation for the solitary waves interaction of the “good” Boussinesq equation . Appl. Numer. Math. , 45 : 161 – 173 .
- Fan , E. and Hon , Y. C. 2003 . A series of traveling wave solutions for two variant Boussinesq equations in shallow water waves . Chaos Soliton Frac. , 15 : 559 – 566 .
- Frutos , J. D.E. , Ortega , T. and Sanz-Serna , J. M. 1991 . Pseudospectral methods for the “good” Boussinesq equation . Math. Comput. , 57 : 109 – 122 .
- Huang , Z. , Jin , S. , Markowich , P. A. and Sparber , C. 2005 . A time-splitting spectral scheme for the Maxwell-Dirac system . J. Comput. Phys. , 208 : 761 – 789 .
- Li , Y. and Zhang , J. E. 2003 . Bidirectional soliton solutions of the classical Boussinesq system and AKNS system . Chaos Soliton Frac. , 16 : 271 – 277 .
- McLachlan , R. I. and Quispel , G. R.W. 2002 . Splitting methods . Acta Numer. , 11 : 341 – 434 .
- Muslu , G. M. and Erbay , H. A. 2003 . A split-step Fourier method for the complex modified Korteweg-de Vries equation . Comput. Math. Appl. , 45 : 503 – 514 .
- Muslu , G. M. and Erbay , H. A. 2005 . Higher-order split-step Fourier schemes for the generalized Schrödinger equation . Math. Comput. Simul. , 67 : 581 – 595 .
- Ortega , T. and Sanz-Serna , J. M. 1990 . Nonlinear stability and convergence of finite-difference methods for the “good” Boussinesq equation . Numer. Math. , 58 : 215 – 229 .
- Pelloni , B. and Dougalis , V. A. 2001 . Numerical modeling of two-way propagation of nonlinear dispersive waves . Math. Comput. Simul. , 55 : 595 – 606 .
- Rong , H. and Liu , R. X. 2004 . Numerical methods for bi-directional soliton problems . J. Univ. Sci. Tech. China , 34 : 295 – 306 .
- Sanders , B. F. , Katopodes , N. D. and Boyd , J. P. 1998 . Spectral modeling of nonlinear dispersive waves . J. Hydraulic Eng. , 124 : 2 – 12 .
- Strang , G. 1968 . On the construction and comparison of difference scheme . SIAM J. Numer. Anal. , 5 : 506 – 517 .
- Tappert , F. 1974 . “ Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method ” . In Nonlinear Wave Motion , Edited by: Newell , A. C. Vol. 15 , 215 – 216 . Providence, RI : Lect. Appl. Math., Amer. Math. Soc. .
- Whitham , G. B. 1999 . Linear and Nonlinear Waves , New York : Wiley .
- Wu , T. Y. and Zhang , J. E. 1996 . “ On modeling nonlinear long waves ” . In Mathematics is for Solving Problems , Edited by: Cook , L. P. , Royturb , V. and Tubin , M. 233 – 241 . Philadelphia : SIAM .
- Zhang , J. E. and Li , Y. 2003 . Bidirectional solitons on water . Phys. Rev. E , 67 : 016306
- Zhang , J. E. , Chen , C. and Li , Y. 2004 . On Boussinesq models of constant depth . Phys. Fluids , 16 : 1287 – 1296 .