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New acoustic wave behaviors to the Davey–Stewartson equation with power-law nonlinearity arising in fluid dynamics

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Abstract

This manuscript investigates the new acoustic wave behaviors of the Davey–Stewartson equation with power-law nonlinearity with the help of sine-Gordon expansion method. This technique yields many new acoustic wave behaviors such as hyperbolic, exponential and complex function structures to the problem considered. Wolfram Mathematica 9 has been used throughout the paper for mathematical calculations along with obtaining two- and three-dimensional surfaces of results.

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References

  1. Yan, C.: A simple transformation for nonlinear waves. Phys. Lett. A 224, 77–84 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Belgacem, F.B.M., Bulut, H., Baskonus, H.M., Akturk, T.: Mathematical analysis of the generalized Benjamin and Burger-KdV equations via the extended trial equation method. J. Assoc. Arab Univ. Basic Appl. 16, 91–100 (2014)

    Google Scholar 

  3. Yan, Z., Zhang, H.: New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics. Phys. Lett. A 252, 291–296 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bulut, H., Aktürk, T., Gürefe, Y.: An application of the new function method to the generalized double sinh-Gordon equation. AIP Conference Proceedings, vol. 1648, 370014-(1-4) (2015)

  5. Zhen-Ya, Y., Hong-Oing, Z., En-Gui, F.: New explicit and travelling wave solutions for a class of nonlinear evaluation equations. Acta Phys. Sin. 48(1), 1–5 (1999)

    MATH  Google Scholar 

  6. Bulut, H.: Classification of exact solutions for generalized form of \(K(m,n)\) equation. Abstract and applied analysis, 2013, Article ID: 742643, p. 11 (2013)

  7. Özpinar, F., Baskonus, H.M., Bulut, H.: On the complex and hyperbolic structures for the (2+1)-dimensional Boussinesq water equation. Entropy 17(12), 8267–8277 (2015)

    Article  Google Scholar 

  8. Baskonus, H.M., Bulut, H.: New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics. Entropy 17(6), 4255–4270 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ergören, H., Sakar, M.G.: Boundary value problems for impulsive fractional differential equations with nonlocal conditions. Adv. Appl. Math. Approx. Theory 41, 283–297 (2013)

    Article  MathSciNet  Google Scholar 

  10. Koç Altan, D., Baskonus, H.M, Bulut, H.: Dark and new travelling wave solutions to the nonlinear evolution equation. In: First International Symposium on Computational Mathematics and Engineering Sciences. Errachidia/Morocco, 03-06 March (2016)

  11. Sakar, M.G., Erdogan, F.: The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian’s decomposition method. Appl. Math. Modell. 37(20), 8876–8885 (2013)

    Article  MathSciNet  Google Scholar 

  12. Sakar, M.G., Ergören, H.: Alternative variational iteration method for solving the time-fractional Fornberg-Whitham equation. Appl. Math. Model. 39(14), 3972–3979 (2015)

    Article  MathSciNet  Google Scholar 

  13. Zakharov, V.E., Schulman, E.I.: Degenerated dispersion laws, motion invariant and kinetic equations. Physica 1D, 185–250 (1980)

    MathSciNet  MATH  Google Scholar 

  14. Davey, A., Stewartson, K.: On three dimensional packets of surface waves. Proc. R. Soc. A 338(1613), 101–110 (1974)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Chow, K.W., Lou, S.Y.: Propagating wave patterns and ‘peakons’ of the Davey- Stewartson system. Chaos, Solitons Fractals 27, 561–567 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ohta, Y., Yang, J.: Dynamics of rogue waves in the Davey-Stewartson II equation. arXiv:1212.0152v1 [nlin.SI]. Accessed on 1 Dec (2012)

  19. 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(3), 1223–1234 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  21. Shen, S., Jiang, L.: The Davey-Stewartson equation with sources derived from nonlinear variable separation method. J. Comput. Appl. Math. 233, 585–589 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ebadi, G., Biswas, A.: The \({{G}^{\prime }}/G\) method and 1-soliton solution of the Davey-Stewartson equation. Math. Comput. Modell. 53, 694–698 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chen, S., Grelu, P., Soto-Crespo, J.M.: Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance. Phys. Rev. E 89, 011201 (2014)

    Article  Google Scholar 

  24. Nistazakis, H.E., Frantzeskakis, D.J., Balourdos, P.S., Tsigopoulos, A., Malomed, B.A.: Dynamics of anti-dark and dark solitons in (2+1)-dimensional generalized nonlinear Schrödinger equation. Phys. Lett. A 278, 68–76 (2000)

    Article  MathSciNet  Google Scholar 

  25. Crosta, M., Fratalocchi, A., Trillo, S.: Bistability and instability of dark-anti dark solitons in the cubic-quintic nonlinear Schrödinger equation. Phys. Rev. A 84, 063809 (2011)

    Article  Google Scholar 

  26. Beyer, W.H.: CRC Standard Mathematical Tables, 28th edn. CRC Press, Boca Raton (1987)

    MATH  Google Scholar 

  27. Weisstein, E.W.: Concise Encyclopedia of Mathematics, 2nd edn. CRC, New York (2002)

    MATH  Google Scholar 

  28. Atangana, A., Baleanu, D.: On the modified groundwater equation under a confined aquifer. Press in Romanian Journal of Physics (2015)

  29. Atangana, A.: On the stability and convergence of the time-fractional variable order telegraph equation. J. Comput. Phys. 293, 104–114 (2015)

    Article  MathSciNet  Google Scholar 

  30. Atangana, A.: Extension of the modified homotopy perturbation method for attractor one-dimensional Keller-Segel equations. J. Appl. Math. Model. 39(10–11), 2909–2916 (2015)

    Article  MathSciNet  Google Scholar 

  31. Atangana, A.: A novel model for the Lassa hemorrhagic fever: deathly disease for pregnant women. Neural Comput. Appl. 26(8), 1895–1903 (2015)

    Article  Google Scholar 

  32. Atangana, A., Alabaraoye, E.: A possible modification of groundwater flow equation. Water Sci. Technol. Water Supply 15(2), 278–287 (2015)

    Article  Google Scholar 

  33. Atangana, A., Goufo, E.F.D.: A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative. J. Nonlinear Sci. Appl. (2015) (in press)

  34. Goufo, E.F.D., Atangana, A.: Extension of fragmentation process in a kinetic-diffusive-wave system. J. Therm. Sci. 19(1), S13–S23 (2015)

  35. Atangana, A.: On the stability of iteration methods for special solution of time-fractional generalized nonlinear ZK-BBM equation. J. Vib. Control 22(7), 1769–1776 (2014)

    Article  MathSciNet  Google Scholar 

  36. Atangana, A.: Drawdown in prolate spheroidal-spherical coordinates obtained via Green’s function and perturbation methods. Commun. Nonlinear Sci. Numer. Simul. 19(5), 1259–1269 (2014)

    Article  MathSciNet  Google Scholar 

  37. Atangana, A.: Convergence and stability analysis of a novel iteration method for fractional biological population equation. Neural Comput. Appl. 25(5), 1021–1030 (2014)

    Article  MathSciNet  Google Scholar 

  38. Bulut, H.: Analytical And Numerical Methods For Solving Nonlinear Partial Differential Equations-I, 1st International Symposium on Computational Mathematics and Engineering Sciences. Errachidia/Morocco, 03-06 March (2016)

  39. Başkonuş, H.M., Bulut, H.: Analytical studies on the (1+1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation defined by seismic sea waves. Waves Random Compl. Media (2015). doi:10.1080/17455030.1062577

  40. Baskonus, H.M., Altan Koç, D., Bulut, H.: New travelling wave prototypes to the nonlinear Zakharov-Kuznetsov equation with power law nonlinearity. Nonlinear Sci. Lett. A: Math. Phys. Mech. 7(2), 67–76 (2016)

    Google Scholar 

  41. Baskonus, H.M., Bulut, H.: New wave behaviors of the system of equations for the ion sound and langmuir waves. Waves Random Compl. Media (2016). doi:10.1080/17455030.2016.1181811

  42. Baskonus, H.M., Bulut, H., Atangana, A.: On the complex and hyperbolic structures of longitudinal wave equation in a magneto-electro-elastic circular rod. Smart Mater. Struct. 25(3), 035022(8) (2016)

  43. Baskonus, H.M., Bulut, H.: Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics. Waves Rand. Compl. Media 26(2), 201–208 (2016)

    MathSciNet  Google Scholar 

  44. Baskonus, H.M., Bulut, H.: On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method. Waves Random Compl. Media 25(4), 720–728 (2015)

    Article  MathSciNet  Google Scholar 

  45. Baskonus, H.M., Altan Koç, D., Bulut, H.: New dark soliton structures to the Newell-Whitehead equation. International Conference on Mathematics and Mathematics Education (ICMME-2016), Elazig/Turkey, 12–14 May (2016)

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  1. Department of Computer Engineering, Faculty of Engineering, Tunceli University, Tunceli, Turkey

    Haci Mehmet Baskonus

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  1. Haci Mehmet Baskonus
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Correspondence to Haci Mehmet Baskonus.

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Baskonus, H.M. New acoustic wave behaviors to the Davey–Stewartson equation with power-law nonlinearity arising in fluid dynamics. Nonlinear Dyn 86, 177–183 (2016). https://doi.org/10.1007/s11071-016-2880-4

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