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Section B

Solitary-wave solutions of the Degasperis–Procesi equation by means of the homotopy analysis method

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Pages 2303-2313 | Received 24 Nov 2007, Accepted 04 Nov 2008, Published online: 20 May 2010

References

  • Abbasbandy , S. 2006 . The application of homotopy analysis method to nonlinear equations arising in heat transfer . Phys. Lett. A , 360 : 109 – 113 .
  • Abbasbandy , S. 2007 . The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation . Phys. Lett. A , 361 : 478 – 483 .
  • Abbasbandy , S. 2007 . Homotopy analysis method for heat radiation equations . Int. Commun. Heat. Mass. Transf. , 34 : 380 – 387 .
  • Abbasbandy , S. 2008 . Solitary wave solutions to the Kuramoto–Sivashinsky equation by means of the homotopy analysis method . Nonlinear Dynam. , 52 : 35 – 40 .
  • Abbasbandy , S. and Parkes , E. J. The family of inverted-loop solitary wave solutions of the Degasperis–Procesi equation by means of the homotopy analysis method . International Conference on ‘Recent Developments in Fluid Mechanics’ . Islamabad, , Pakistan
  • Abbasbandy , S. and Parkes , E. J. 2008 . Solitary smooth-hump solutions of the Camassa–Holm equation by means of the homotopy analysis method . Chaos, Solitons & Fractals , 36 : 581 – 591 .
  • Abbasbandy , S. and Samadian Zakaria , F. 2008 . Soliton solutions for the fifth-order KdV equation with the homotopy analysis method . Nonlinear Dynam. , 51 : 83 – 87 .
  • Abbasbandy , S. , Tan , Y. and Liao , S. J. 2007 . Newton-Homotopy analysis method for nonlinear equations . Appl. Math. Comput. , 188 : 1794 – 1800 .
  • Degasperis , A. , Holm , D. and Hone , A. 2002 . A new integrable equation with peakon solutions . Theor. Math. Phys. , 133 : 1461 – 1472 .
  • Hayat , T. and Khan , M. 2005 . Homotopy solutions for a generalized second-grade fluid past a porous plate . Nonlinear Dynam. , 42 : 395 – 405 .
  • Hayat , T. , Khan , M. and Ayub , M. 2005 . On non-linear flows with slip boundary condition . Z. Angew. Math. Phys. (ZAMP) , 56 : 1012 – 1029 .
  • Lenells , J. 2005 . Traveling wave solutions of the Camassa–Holm equation . J. Differen. Eq. , 217 : 393 – 430 .
  • Lenells , J. 2005 . Traveling wave solutions of the Degasperis–Procesi equation . J. Math. Anal. Appl. , 306 : 72 – 82 .
  • Liao , S. J. 2003 . Beyond Perturbation: Introduction to the Homotopy Analysis Method , Boca Raton : Chapman & Hall/CRC Press .
  • Liao , S. J. 2005 . A new branch of solutions of boundary-layer flows over an impermeable stretched plate . Int. J. Heat. Mass. Transfer. , 48 : 2529 – 2539 .
  • Liao , S. J. 2006 . Series solutions of unsteady boundary-layer flows over a stretching flat plate . Stud Appl Math. , 117 : 239 – 264 .
  • Liao , S. J. and Cheung , K. 2003 . Homotopy analysis of nonlinear progressive waves in deep water . J. Eng. Math. , 45 : 105 – 116 .
  • Liao , S. J. and Magyari , E. 2006 . Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones . Z. Angew. Math. Phys. (ZAMP) , 57 : 777 – 792 .
  • Liao , S. J. , Su , J. and Chwang , A. T. 2006 . Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body . Int. J. Heat. Mass. Transfer. , 49 : 2437 – 2445 .
  • Parkes , E. J. and Abbasbandy , S. 2009 . Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method . Numer. Methods Partial Differen. Eq. , 25 : 401 – 408 .
  • Parkes , E. J. and Vakhnenko , V. O. 2005 . Explicit solutions of the Camassa–Holm equation . Chaos, Solitons & Fractals , 26 : 1309 – 1316 .
  • Sajid , M. , Hayat , T. and Asghar , S. 2006 . On the analytic solution of the steady flow of a fourth grade fluid . Phys. Lett. A , 355 : 18 – 26 .
  • Tan , Y. and Abbasbandy , S. 2008 . Homotopy analysis method for quadratic Riccati differential equation . Commun. Nonlinear Sci. Numer. Simul. , 13 : 539 – 546 .
  • Tan , Y. , Xu , H. and Liao , S. J. 2007 . Explicit series solution of travelling waves with a front of Fisher equation . Chaos, Solitons & Fractals , 31 : 462 – 472 .
  • Vakhnenko , V. O. and Parkes , E. J. 2004 . Periodic and solitary–wave solutions of the Degasperis–Procesi equation . Chaos, Solitons & Fractals , 20 : 1059 – 1073 .
  • Wang , C. 2006 . Analytic solutions for a liquid film on an unsteady stretching surface . Heat. Mass. Transf. , 42 : 759 – 766 .
  • Wu , W. and Liao , S. J. 2005 . Solving solitary waves with discontinuity by means of the homotopy analysis method . Chaos, Solitons & Fractals , 26 : 177 – 185 .

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