Publication Cover
Applicable Analysis
An International Journal
Volume 57, 1995 - Issue 1-2
55
Views
24
CrossRef citations to date
0
Altmetric
Original Articles

Travelling wave solutions for nonlinear dispersive equations with dissipation

Pages 85-100 | Received 05 Jun 1994, Published online: 02 May 2007

  • Arrigo , D.J. , Braodbridge , P. and Hill , J.M. 1993 . Nonclassical symmetry solutions and the methods of Bluman-Cole and Clarkson-Kruskal . J.Math. Phys. , 34 ( 10 ) : 4692 – 4703 .
  • Berkovich , L.M. and Nechaevsky , M.L. 1983 . On group features and integrability of the Emden-Fowler type equations. . In: "Group theoretical methods in physics , 2 : 463 – 471 .
  • Bluman , G.W. and Cole , J.D. 1974 . Similarity methods for differential equations , Berlin : Springer .
  • Clarkson , P.A. 1989 . New similarity reductions of the Boussinesq equation. . J.Math.Phys. , 30 ( 10 ) : 2201 – 2213 .
  • Clarkson , P.A. and Winternitz , P. 1991 . Physica D , 49 : 257
  • Engelbrecht , J. 1991 . An introduction to asymmetric solitary waves . London, Longman ,
  • Golubev , V. 1941 . Lessons on analytical theory of differential equations . Moscow-Leningrad, GITTL , : 400
  • Gundersen , R. 1990 . Travelling wave solutions of nonlinear partial differential equations. . Int. J.Engng. Math. , 24 : 323 – 341 .
  • Hermite , C. 1873 . Course Lithographie de I'Ecole Polytechnique Paris
  • Hunter , J.K. and Scheurle , J. 1998 . Existence of perturbed solitary wave solutions to a model equation for water waves. . Physica D , 32 : 253 – 268 .
  • Ince , E.L. , Jeffrey , A. and Xu , S. 1989 . Exact solutions to the Korteweg-de Vries-Burgers equation . Wave Motion , 11 : 559 – 564 .
  • Kashcheev , V.N. 1956 . Heuristic methods of finding the solutions for nonlmear solitonics equations Dover, NY Rige, Zinatne ,1990
  • Kudryashov , N.A. 1988 . Sov.Math.-Doklady , 300 ( 2 ) : 342 – 345 .
  • Lemke , H. 1920 . Sitzungsberichte Berlin Math . Gesell , 18 : 26
  • Malmquist , I. 1914 . Sur le fonctionsà un nombre fini de branches définies par leséquations diffréntielles du premier ordre. . Acta Math. , 36 : 310
  • McIntosh , I. 1990 . Single phase averaging and travelling wave solutions of the modified Burgers-Korteweg-de Vries equation. . Phys.Letters A , 143 ( 1-2 ) : 57 – 61 .
  • Nucci , M.C. and Clarkson , P.A. 1992 . The nonclassical method is more general than the direct method for symmetry reductions. An example of the Fitzhugh-Nagumo equation. . Phys.Letters A , 164 : 49 – 56 .
  • Poincaré , H. 1885 . Sur un théoremé de M.Fuchs. . Acta Math. , 7 : 7
  • Samsonov , A.M. and Samsonov , A.M. 1988 . On existence of longitudinal strain solitons in an infinite nonlinearly elastic rod . Sov.Physics- Doklady , 33 ( 4 ) : 298 – 300 .
  • Samsonov , A.M. 1988 . “ On some exact travelling wave solutions for nonlinear hyperbolic equations, ” . In "Nonlinear waves and dissipative effects" 123 – 132 . Bologna Longman, London ,1991
  • Samsonov , A.M. 1993 . “ Some exact wave solutions in terms of the Weierstrass functions for nonlinear hyperbolic equations. In: ” . In Future directions of nonlinear dynamics in physical and biological systems Edited by: Christiansen , P.L. , Eilbeck , J.C. and Parmentier , R.D. 125 – 128 . New York
  • Vlieg-Hulstman , M. and Halford , W. 1991 . The Korteweg-de Vries-Burgers' equation: a reconstruction of exact solutions . Wave Motion , 14 : 267 – 271 .
  • Whittaker , E.E. and Watson , G.M. 1927 . Modern analysis , Cambridge, The University press .
  • Xiong , S.L. 1989 . An analytic solution of Burgers-KdV equation . Chinese Sci. Bull. , 34 : 1158 – 1162 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.