71
Views
0
CrossRef citations to date
0
Altmetric
Section B

Exact periodic, cusp, solitary and loop wave solutions of the EX-ROE

&
Pages 2824-2837 | Received 19 Oct 2008, Accepted 22 Dec 2010, Published online: 09 Jun 2011

References

  • Boyd , J. P. 2005 . Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: Matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves) . Eur. J. Appl. Math. , 16 : 65 – 81 .
  • Byrd , P. F. and Friedman , M. D. 1971 . “ Handbook of Elliptic Integrals for Engineers and Scientists ” . Berlin : Springer .
  • Espinosa , A. and Fujioka , J. 1994 . Hydrodynamic foundation and Painleve analysis of Hirota–Satsuma-type equations . J. Phys. Soc. Japan. , 63 : 1289 – 1294 .
  • Li , J. B. 2007 . Dynamical understanding of loop soliton solution for several nonlinear wave equations . Sci. China Ser. , A 50 : 773 – 785 .
  • Liu , Y. P. , Li , Z. B. and Wang , K. C. 2007 . Symbolic computation of exact solutions for a nonlinear evolution equation . Chaos, Solitons and Fractals. , 31 : 1173 – 1180 .
  • Ma , Y. L. , Li , B. Q. and Wang , C. 2009 . A series of abundant exact travelling wave solutions for a modified generalized Vakhnenko equation using auxiliary equation method . Appl. Math. Comput. , 211 : 102 – 107 .
  • Morrison , A. J. and Parkes , E. J. 2003 . The N-soliton solution of the modified generalized Vakhnenko equation (a new nonlinear evolution equation) . Chaos Solitons and Fractals. , 16 : 13 – 26 .
  • Morrison , A. J. , Parkes , E. J. and Vakhnenko , V. O. 1999 . The N loop soliton solution of the Vakhnenko equation . Nonlinearity , 12 : 1427 – 1437 .
  • Ostrovsky , L. A. 1978 . Nonlinear internal waves in a rotating ocean . Oceanology , 18 : 119 – 125 .
  • Parkes , E. J. 1993 . The stability of solutions of Vakhnenkos equation . J. Phys. A: Math. Gen. , 26 : 6469 – 6475 .
  • Parkes , E. J. 2007 . Explicit solutions of the reduced Ostrovsky equation . Chaos Solitons Fractals , 31 : 602 – 610 .
  • Parkes , E. J. 2008 . Periodic and solitary travelling-wave solutions of an extended reduced ostrovsky equation . SIGMA 4 , 053 : 1 – 17 .
  • Stepanyants , Y. A. 2006 . On stationary solutions of the reduced Ostrovsky equation: Periodic waves, compactons and compound solitons . Chaos Solitons Fractals , 28 : 193 – 204 .
  • Stepanyants , Y. A. 2008 . Solutions classification to the extended reduced Ostrovsky equation . SIGMA 4 , 073 : 1 – 19 .
  • Vakhnenko , V. A. 1992 . Solitons in a nonlinear model medium . J. Phys. A: Math. Gen. , 25 : 4181 – 4187 .
  • Vakhnenko , V. A. 1999 . High-frequency soliton-like waves in a relaxing medium . J. Math. Phys. , 40 : 2011 – 2020 .
  • Xie , S. L. and Cai , J. H. 2009 . Exact compacton and generalized kink wave solutions of the extended reduced Ostrovsky equation . Commun. Nonlinear Sci. Numer. Simul. , 14 : 3561 – 3573 .
  • Xie , S. L. , Rui , W. G. and Hong , X. C. 2006 . The compactons and generalized kink waves to a generalized Camassa-Holm equation . Rostock. Math. Kolloq. , 61 : 31 – 48 .

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.