Decay of solutions of a Boussinesq-type system with variable coefficients

References

• Quintero , JR and Muñoz Grajales , JC . 2004 . Existence and uniqueness for a system of Boussinesq equations . Methods Appl. Anal. , 11 : 15 – 32 .
   Google Scholar
• Muñoz Grajales , JC and Nachbin , A . 2006 . Improved Boussinesq-type equations for highly variable depth . IMA J. Appl. Math. , 71 : 600 – 633 .
   Google Scholar
• Antonopoulos , DC , Dougalis , VA and Mitsotakis , DE . 2010 . Numerical solution of Boussinesq systems of the Bona-Smith family . Appl. Num. Math. , 60 : 314 – 336 .
   Google Scholar
• Bona , J and Chen , M . 1998 . A Boussinesq system for two-way propagation of nonlinear dispersive waves . Physica D , 116 : 191 – 224 .
   Google Scholar
• Bona , J and Chen , H . 2002 . Solitary waves in nonlinear dispersive systems . Discrete Contin. Dyn. Syst. Ser. B , 2 : 313 – 378 .
   Google Scholar
• Chen , M . 2000 . Solitary-wave and multi-pulsed travelling-wave solutions of a Boussinesq system . Appl. Anal. , 75 ( 1–2 ) : 213 – 240 .
   Google Scholar
• Chen , H , Chen , M and Nguyen , NV . 2007 . Cnoidal wave solutions to Boussinesq systems . Nonlinearity , 20 : 1443 – 1461 .
   Google Scholar
• Dougalis , VA , Durán , A and López-Marcos , MA . 2007 . A numerical study of the stability of solitary waves of the Bona-Smith family of Boussinesq systems . Nonlinear Sci. , 17 : 569 – 607 .
   Google Scholar
• Ben-Yu , G and Zhong-Qing , W . Modified Chebyshev rational spectral method for the whole line, Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, May 24–27, (2002), pp. 365–374
   Google Scholar
• Muñoz Grajales , JC and Rivas , I . 2008 . Existence and asymptotic decay for a Boussinesq-type model . J. Math. Anal. Appl. , 345 : 455 – 475 .
   Google Scholar
• Garnier , J , Muñoz Grajales , JC and Nachbin , A . 2007 . Effective behavior of solitary waves over random topography . Multiscale Model. Simul. , 6 ( 3 ) : 995 – 1025 .
   Google Scholar
• Enquist , B and Majda , A . 1977 . Absorbing boundary conditions for the numerical simulation of waves . Math. Comp. , 31 ( 139 ) : 629 – 651 .
   Google Scholar
• Muñoz Grajales , JC and Nachbin , A . 2004 . Dispersive wave attenuation due to orographic forcing . SIAM J. Appl. Math. , 64 : 977 – 1001 .
   Google Scholar
• Nwogu , O . 1993 . Alternative form of Boussinesq equations for nearshore wave propagation . J. Waterway, Port, Coastal Ocean Eng. , 119 : 618 – 638 .
   Google Scholar
• Wei , G and Kirby , J . 1995 . Time-dependent numerical code for extended Boussinesq equations . J. Waterway, Port, Coastal Ocean Eng. , 121 ( 5 ) : 251 – 261 .
   Google Scholar
• Larsen , J and Dancy , H . 1983 . Open boundaries in short wave simulations – A new approach . Coast. Eng. , 7 : 285 – 297 .
   Google Scholar
• Yoon , SB and Choi , JW . 2001 . A note on extension of fully dispersive weakly nonlinear wave equations for rapidly varying topography . Coast. Eng. , 43 ( 3 ) : 143 – 160 .
   Google Scholar
• Asch , M , Kohler , W , Papanicolaou , G , Postel , M and White , B . 1991 . Frequency content of randomly scattered signals . SIAM Review , 33 : 519 – 626 .
   Google Scholar
• O'Doherty , RF and Anstey , NA . 1971 . Reflections on amplitudes . Geophys. Prospect. , 19 : 430 – 458 .
   Google Scholar
• Berlyand , L and Burridge , R . 1995 . The accuracy of the O'Doherty–Anstey approximation for wave propagating in highly disordered stratified media . Wave Motion , 21 : 357 – 373 .
   Google Scholar
• Burridge , R , Papanicolaou , G and White , B . 1988 . One-dimensional wave propagation in a highly discontinuous medium . Wave Motion , 10 : 19 – 44 .
   Google Scholar
• Clouet , J-F and Fouque , J-P . 1994 . Spreading of a pulse traveling in random media . Ann. Appl. Prob. , 4 : 1083 – 1097 .
   Google Scholar
• Lewicki , P . 1994 . Long-time evolution of wavefronts in random media . SIAM J. Appl. Math. , 54 : 907 – 934 .
   Google Scholar
• Lewicki , P , Burridge , R and Papanicolaou , G . 1994 . Pulse stabilization in a strongly heterogeneous medium . Wave Motion , 20 : 177 – 195 .
   Google Scholar
• Fouque , JP , Garnier , J and Nachbin , A . 2004 . Time-reversal for dispersive waves in random media . SIAM J. Appl. Math. , 64 : 1810 – 1838 .
   Google Scholar
• Nachbin , A . 2003 . A terrain-following Boussinesq system . SIAM J. Appl. Math. , 63 : 905 – 922 .
   Google Scholar
• Chen , M . 1998 . Exact solutions of various Boussinesq systems . Appl. Math. Lett. , 11 ( 5 ) : 45 – 49 .
   Google Scholar
• Driscol , TA . http://www.math.udel.edu/driscoll/software
   Google Scholar
• Driscoll , TA and Trefethen , L . 2002 . Schwarz–Christoffel Mapping , Cambridge : Cambridge University Press .
   Google Scholar