458
Views
29
CrossRef citations to date
0
Altmetric
Original Articles

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

, , , &
Pages 559-590 | Received 10 Jan 2011, Accepted 07 Jul 2011, Published online: 18 Aug 2011

References

  • Babaoglu , C . 2006 . Some special solutions of a generalized Davey–Stewartson system . Chaos, Solitons Fractals , 30 : 781 – 790 .
  • Babaoglu , C . 2008 . Long-wave short-wave resonance case for a generalized Davey–Stewartson system . Chaos, Solitons Fractals , 38 : 48 – 54 .
  • Caixia , S and Boling , G . 2008 . Ill-posedness for the nonlinear Davey–Stewartson equation . Acta Mathematica Scientia , 28 : 117 – 127 .
  • Chow , KW and Lou , SY . 2006 . Propagating wave patterns and ‘peakons’ of the Davey–Stewartson system . Chaos, Solitons Fractals , 27 : 561 – 567 .
  • Ebadi , G and Biswas , A . 2011 . The G′/G method and 1-soliton solution of Davey–Stewartson equation . Math. Comput. Model. , 53 : 694 – 698 .
  • Eden , A , Erbay , HA and Muslu , GM . 2008 . Closing the gap in the purely elliptic generalized Davey–Stewartson system . Nonlinear Anal.: Theory, Meth. Appl. , 69 : 2575 – 2582 .
  • He , JH . 1997 . Variational iteration method for delay differential equation . Commun. Nonlinear Sci. Numer. Simul. , 2 : 2350 – 2356 .
  • He , JH . 1999 . Variational iteration method – A kind of nonlinear analytical technique some examples . Internat. J. Nonlinear Mech. , 34 : 699 – 708 .
  • He , JH . 2006 . Some asymptotic methods for strongly nonlinear equations . Internat. J. Mod. Phys. B , 20 : 1141 – 1199 .
  • He , JH . 2007 . Variational iteration method – Some recent results and new interpretations . J. Comput. Appl. Math. , 207 : 3 – 17 .
  • He , JH , Wu , GC and Austin , F . 2010 . The variational iteration method which should be followed . Nonlinear Sci. Lett. A , 1 : 1 – 30 .
  • Jafari , H and Alipour , M . 2010 . Numerical solution of the Davey–Stewartson equations using variational iteration method . World Appl. Sci. J. , 8 : 814 – 819 .
  • Jalilian , Y . 2008 . A variational iteration method for solving systems of partial differential equations and for numerical simulation of the reaction-diffusion brusselator model . Scientia Iranica , 15 : 223 – 229 .
  • Jaulent , M , Manna , MA and Martinez-Alonso , L . 1990 . Fermionic analysis of Davey–Stewartson dromions . Phys. Lett. A , 151 : 303 – 307 .
  • Krishnan , EV and Biswas , A . 2010 . Solutions of the Zakharov–Kuznetsov equation with higher order nonlinearity by mapping and ansatz method . Phys. Wave Phenom , 18 : 256 – 261 .
  • Krishnan , EV and Peng , Y . 2006 . Exact solutions to the combined KdV–mKdV equation by the extended mapping method . Physica Scripta , 73 : 405 – 409 .
  • Labidi , M and Omrani , K . 2011 . Numerical simulation of the modified regularized long wave equation by He's variational iteration method . Numer. Meth. Partial Differ. Equ. , 27 : 478 – 489 .
  • Labidi , M and Omrani , K . 2011 . The use of variational iteration method and homotopy perturbation method for solving two nonlinear partial differential equations . Internat. J. Numer. Meth. Heat Fluid Flow , 21 : 377 – 398 .
  • Osborne , A . 2010 . Modeling the Davey–Stewartson (DS) equations . Internat. Geophys. , 97 : 867 – 875 . Chapter 34
  • Pang , GD . 1993 . Conservation laws of the quantized Davey–Stewartson-II system . Phys. Lett. A , 173 : 228 – 232 .
  • Tang , XY , Chow , KW and Rogers , C . 2009 . Propagating wave patterns for the ‘resonant’ Davey–Stewartson system . Chaos, Solions Fractals , 42 : 2707 – 2712 .
  • Tatari , M and Dehghan , M . 2009 . Improvement of He's variational iteration method for solving systems of differential equations . Comput. Math. Appl. , 58 : 2160 – 2166 .
  • Wang , Y . 2010 . The Cauchy problem for the elliptic-hyperbolic Davey–Stewartson equation in Sobolev space . J. Math. Anal. Appl. , 367 : 174 – 192 .
  • Wazwaz , A-M . 2007 . The variational iteration method for solving linear and nonlinear systems of PDEs . Comput. Math. Appl. , 54 : 895 – 902 .
  • Yan , Z . 2003 . Abundant families of Jacobi elliptic function solution of the (2 + 1)-dimensional integrable Davey–Stewartson type equation via a new method . Chaos, Solitons Fractals , 18 : 299 – 309 .
  • Zheng-De , D , Wang , C-J , Lin , S-Q , Li , D-L and Mu , G . 2010 . The three-wave method for nonlinear evolution equations . Nonlinear Sci. Lett. A , 1 : 77 – 82 .

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.