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New soliton solutions of Davey–Stewartson equation with power-law nonlinearity

Optical and Quantum Electronics volume 49, Article number: 117 (2017) Cite this article

Abstract

This study is related to new soliton solutions of Davey–Stewartson equation (DSE) with power-law nonlinearity. The generalized Kudryashov method which is one of the analytical methods has been used for finding exact solutions of this equation. By using this method, dark soliton solutions of DSE have been found. Also, by using Mathematica Release 9, some graphical representations have been done to analyze the motion of these solutions.

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References

  • Ablowitz, M.J., Biondini, G., Blair, S.: Nonlinear Schrödinger equations with mean terms in nonresonant multidimensional quadratic materials. Phys. Rev. E 63(4), 466051–4660515 (2001)

    Article  Google Scholar 

  • Babaoglu, C.: Long-wave short-wave resonance case for a generalized Davey–Stewartson system. Chaos Solitons Fractals 38, 48–54 (2008)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  • Bashir, M.A., Moussa, A.A.: The cotha(ξ) expansion method and its application to the Davey–Stewartson equation. Appl. Math. Sci. 8(78), 3851–3868 (2014)

    Article  Google Scholar 

  • Baskonus, H.M., Bulut, H.: On some new analytical solutions for the (2 + 1)-dimensional Burgers equation and the special type of Dodd–Bullough–Mikhailov equation. J. Appl. Anal. Comput. 5(4), 613–625 (2015)

    MathSciNet  Google Scholar 

  • Chang, L., Pan, Y., Ma, X.: New exact travelling wave solutions of Davey–Stewartson equation. J. Comput. Inf. Syst. 9(4), 1687–1693 (2013)

    Google Scholar 

  • Davey, A., Stewartson, K.: On three-dimensional packets of surface waves. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 338(1613), 101–110 (1974)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  • Ebadi, G., Biswas, A.: The G′/G method and 1-soliton solution of the Davey–Stewartson equation. Math. Comput. Model. 53, 694–698 (2011)

    MathSciNet  Article  MATH  Google Scholar 

  • Ebadi, G., Krishnan, E.V., Labidi, M., Zerrad, E., Biswas, A.: Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity. Waves Random Complex Media 21(4), 559–590 (2011)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  • El-Ganaini, S.I.A.: New exact solutions of some nonlinear systems of partial differential equations using the first integral method. Abstr. Appl. Anal. 2013, 1–13 (2013)

    MathSciNet  MATH  Google Scholar 

  • El-Kalaawy, O.H., Ibrahim, R.S.: Solitary wave solution of the two-dimensional regularized long-wave and Davey–Stewartson equations in fluids and plasmas. Appl. Math. 3, 833–843 (2012)

    Article  Google Scholar 

  • Eslami, M., Mirzazadeh, M.: Functional variable method to study nonlinear evolution equations. Cent. Eur. J. Eng. 3(3), 451–458 (2013)

    Google Scholar 

  • Gurefe, Y., Misirli, E., Pandir, Y., Sonmezoglu, A., Ekici, M.: New exact solutions of the Davey–Stewartson equation with power-law nonlinearity. Bull. Malays. Math. Sci. Soc. 38, 1223–1234 (2015)

    MathSciNet  Article  MATH  Google Scholar 

  • Jafari, H., Sooraki, A., Talebi, Y., Biswas, A.: The first integral method and traveling wave solutions to Davey–Stewartson equation. Nonlinear Anal. Model. Control 17(2), 182–193 (2012)

    MathSciNet  MATH  Google Scholar 

  • Leblond, H.: Electromagnetic waves in ferromagnets: a Davey–Stewartson-type model. J. Phys. A Math. Gen. 32, 7907–7932 (1999)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  • Song, M., Biswas, A.: Topological defects and bifurcation analysis of the DS equation with power law nonlinearity. Appl. Math. Inf. Sci. 9(4), 1719–1724 (2015)

    MathSciNet  Google Scholar 

  • Tuluce Demiray, S., Pandir, Y., Bulut, H.: New soliton solutions for Sasa–Satsuma equation. Waves Random Complex Media 25(3), 417–428 (2015a)

    ADS  MathSciNet  Article  Google Scholar 

  • Tuluce Demiray, S., Pandir, Y., Bulut, H.: New solitary wave solutions of Maccari system. Ocean Eng. 103, 153–159 (2015b)

    Article  Google Scholar 

  • Tuluce Demiray, S., Bulut, H.: New exact solutions of the new Hamiltonian amplitude equation and Fokas Lenells equation. Entropy 17, 6025–6043 (2015)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  • Tuluce Demiray, S., Pandir, Y., Bulut, H.: All exact travelling wave solutions of Hirota equation and Hirota–Maccari system. Optik 127, 1848–1859 (2016)

    ADS  Article  Google Scholar 

  • Tuluce Demiray, S., Bulut, H.: Generalized Kudryashov method for nonlinear fractional double sinh-Poisson equation. J. Nonlinear Sci. Appl. 9, 1349–1355 (2016)

    MathSciNet  MATH  Google Scholar 

  • Tuluce Demiray, S., Pandir, Y., Bulut, H.: The analysis of the exact solutions of the space fractional coupled KD equations. In: AIP Conference Proceedings, vol 1648, pp. 370013-(1–5) (2015)

  • Zedan, H.: Applications of the new compound Riccati equations rational expansion method and Fan’s subequation method for the Davey–Stewartson equations. Bound. Value Probl. (2010)

  • Zedan, H.A., Monaquel, S.J.: The sine–cosine method for the Davey–Stewartson equations. Appl. Math. E-Notes 10, 103–111 (2010)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Firat University, 23119, Elazig, Turkey

    Seyma Tuluce Demiray & Hasan Bulut

Authors
  1. Seyma Tuluce Demiray
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  2. Hasan Bulut
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Correspondence to Seyma Tuluce Demiray.

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Tuluce Demiray, S., Bulut, H. New soliton solutions of Davey–Stewartson equation with power-law nonlinearity. Opt Quant Electron 49, 117 (2017). https://doi.org/10.1007/s11082-017-0950-6

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  • DOI: https://doi.org/10.1007/s11082-017-0950-6

Keywords

  • Davey–Stewartson equation
  • Generalized Kudryashov method
  • Dark soliton solutions
  • Mathematica Release 9