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Applicable Analysis
An International Journal
Volume 75, 2000 - Issue 1-2
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Original Articles

Solitary-wave and multi-pulsed traveling-wave solutions of boussinesq systems

Pages 213-240 | Received 01 Aug 1999, Published online: 25 Nov 2010

References

  • Amick , C.J. 1984 . Regularity and uniqueness of soluttons to the Boussinesq system of equations . J. Differential Equation , 54 : 231 – 247 .
  • Amick , C.J. and Kirchgassner , k. 1989 . A theoy of solitay water-waves tn the presence of surface tenston . Arch. Rational Mech. Anal , 105 : 1 – 49 .
  • Amick , C.J. and Toland , J.F. 1981 . On solttary waves of finite amplttud . Arch. Rational Mech. Ana , 76 : 9 – 95 .
  • 1992 . Global uniqueness of homoclinic orbits for a class of fourth order equattons . Z. angew Math Phys , 43 : 591 – 597 .
  • Benjamin , T.B. , Bona , J.L. and Bose , D.K. 1990 . Solitary-wave soluttons of nonlinear problems . Phil. Trans. Royal Soc. London , 331 : 195 – 244 .
  • Benjamin , T.B. , Bona , J.L. and Mahony , J.J. 1972 . Model equations for long waves in nonlinear dispersive systems . Phil. Trans. Royal Soc. , 272 : 47 – 78 .
  • Bona , J.L. and Chen , M. 1998 . A Bousstnesq system for two-way propayatton of nonltnear dispersive waves . Physica D , 116 : 191 – 224 .
  • Bona , J.L. , Chen , M. and Saut , J.C. “ Bousstnesq equations for smali-amplitude long wavelength water waves ” .
  • bona , J.L. and Smith , R. 1976 . A model for the two-way propagation of water waves in a channel . Math. Proc. Cambridge Phil. Soc , 79 : 167 – 182 .
  • Boussinesq , J.V. 1871 . Théorie de l'intumescence liquide appelde onde solitire ou de translation se propayeant dans un canal rectangularre . Comptes Rendus de l'acadmie de Sciences , 72 : 755 – 759 .
  • 1871 . Théorie général des mouvements qui sont propagés dans un canal vectanyulatre horwontal. . Comp. Rend. Hebd. des Scances de L'Acadmie de Sciences , 73 : 256 – 260 .
  • 1872 . Théorie des ondes et des remous qui se propagés dans un canal rectangulaire horizontal, en communtquant au ltquide contenu dans ce canal des uitesses senstblement . Journal de Mathkmatiques Pures et Appliquées , 17 : 55 – 108 .
  • Buffon , B. 1995 . Infinitely many large amplitude homoclintc orbits for a class of autonomous hamiltonian systems . J. Diff. Eqns , 121 : 109 – 120 .
  • Champneys , A.R. 1994 . Subsidiary homoclinic orbits to a saddle-focus for reversible systems . Int. J. Bifurcation and Chaos , 4 : 1447 – 1482 .
  • Champneys , A.R. and Groves , M.D. 1997 . A global investigation of solitary-wave solutions to a two-parameter model for water waves . J . Fluid Mech , 342 : 199 – 229 .
  • Champneys , A.R. , Kuznetsove , Y.A. and Sandstede , B. 1996 . A numerical toolbox for homoclinic bifurcation analysts: Internat. . J. Bifur. Chaos Appl. Sci. Engrg , 6 : 867 – 887 .
  • Champneys , A.R. and Spence , A. 1993 . Hunting for homoclinic orbits in reversible systems . A shooting technique, Advances in Computational Mathematics , 1 : 81 – 108 .
  • Toland , J.F. 1993 . Bifurcation ofa plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems. . Nonlinearity , 6 : 665 – 722 .
  • Chen , M. 1998 . Exact solutions of various Boussinesq systems . Appl. Math. Lett , 11 : 45 – 49 .
  • Conte , R. , Musette , M. and Pickering , A. 1994 . Factorization of the “clussical Boussinesq” . system, J. Phys .A , 27 : 2831 – 2836 .
  • Craig , W. and Groves , M.D. 1994 . Hamiltonian long-wave approximations to the water-wave problams . Wave Motions , 19 : 367 – 389 .
  • Doedel , E.J. , Champneys , A.R. , Fairgrieve , T.F. , Kuznetsov , Y.A. , Sandstede , B. and Wang , X.J. “ Continuation and bifurcation software for ordinary differential equations ” . FTP . doedel/auto
  • Groves , M.D. 1998 . Solitary-wave solutions to a class fifth-order model equations . Nonlinearity , 11 : 341 – 353 .
  • Hunt , G.W. , Bolt , H.M. and Thompson , J.M.T. 1989 . Structural localization phenomena and the dynamical phase-space analogy . Proc. Roy. Soc. Lond , 425 : 245 – 267 .
  • Hunt , G.W. and Wadee , M.K. 1991 . Comparative Lagrangian formulations for localized buckling . Proc. R. Sac. Lond , 434 : 485 – 502 .
  • Kaup , D.J. 1975 . A higher-order water-wave equation and the method for solving it . Progress of Theoretical Physics , 54 : 396 – 408 .
  • Krishnan , E.V. 1982 . An exact solution oj the classical Boussinesq equation . J. Phys. Soc , 51 : 2391 – 2392 .
  • Pego , R. and Weinstein , M. 1997 . convective linear stability of solitary waves for Boussinesq equations . Stud. Appl. Math. , 99 ( 4 ) : 311 – 375 .
  • Peregrine , D.H. 1972 . “ Equations for water waves and the approximation behind them, in Waves on beaches and resulting sediment transport ” . In proceedings of an advanced seminar conducted by the Mathematics Research Center , 95 – 121 . New York : Academic Press .
  • Sachs , R.L. 1988 . On the integrable variant of the Boussinesq system: Painlev/'e property, rational solutions, a related many-body system, and equivalence with akns hierarchy . Physica D , 30 : 1 – 27 .
  • Schonbek , M.E. 1981 . Existence of solutions for the Boussinesq system of equations . J. Differential Equations , 42 : 325 – 352 .
  • Teng , M.H. and Wu , T.Y. 1994 . A bidirectional long-wave model . Methuds Appl. Anal , 1 : 108 – 117 .
  • Toland , J.F. 1981 . Solitary wave solutions for a model of the two-way propagation of water waves in a channel . Math.Proc. Camb.Phill.Soc , 90 : 343 – 360 .
  • Toland , J.F. 1984 . Uniqueness and a pirori bounds for certain hormoclinic orbits of a Boussinesq system modeling solitary water wave . Comm. Math. Phys , 94 : 239 – 254 .
  • Toland , J.F. 1986 . Existence of symmetric homoclinic orbits for systems of Eder-Lagrange equations . Proceedings of Symposia in Pure Mathematics , 45 : 447 – 459 .
  • Ton , B.A. 1980 . Initial-value problems for the Boussinesq equations of water waves . Nonlinear Anal , 4 : 15 – 26 .
  • Whitham , G.B. “ Linear and nonlinear waves ” . J.Wiley&Sons .
  • Winther , R. 1982 . A finite element method for a version of the Boussinesq equation . SIAM J. Numer. Anal , 19 : 561 – 570 .

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