Optical soliton solutions of nonlinear Davey-Stewartson equation using an efficient method


  • Hatira Gunerhan Kafkas University




Generalized exponential rational function method, Exact soliton solutions, Davey-Stewartson equation, Optical solutions, Nonlinear Partial differential equations.


One of the most important tools for expressing physical phenomena in the world around us is to express problems using differential equations with partial derivatives. This importance has attracted the attention of many researchers. The result of these considerations has been the invention and application of various analytical and numerical methods in solving this category of equations. In this work, we make use of a newly-developed technique called the generated exponential rational function method to compute the exact solution of the Davey-Stewartson equation. According to all research studies I have done so far, there is no similar research work carried out in the present paper. The results attest to the efficiency of the proposed method. The method used in this paper has the ability to be employed in other cases in solving equations with relative derivatives.


A. Davey, K. Stewartson, On three-dimensional packets of surface waves, Proc. R. Soc. London Ser. A, 338 (1974), 101–110.

C. Babaoglu, ALong-wave short-wave resonance case for a generalized Davey–Stewartson system, Chaos Solitons Fractal, 38(1) (2008), 48–54.

K.W. Chow, S.Y. Lou, Propagating wave patterns and peakons of the Davey–Stewartson system, Chaos Solitons Fractal, 27(2) (2006), 561–567.

M. D. Groves, S-M Sun, E. Wahln, Periodic solitons for the elliptic–elliptic focussing Davey–Stewartson equations, C. R. Acad. Sci. Paris, Ser., I, 354 (2016), 486–492.

R. F. Zinati, J. Manafian, Applications of He’s semi-inverse method, ITEM and GGM to the Davey-Stewartson equation, Eur. Phys. J. Plus., 132 (2017), 155.

G. Ebadi, A. Biswas, The G0=G method and 1-soliton solution of the Davey–Stewartson equation, Math. Comput. Model., 53 (2011), 694–698.

Y. Gao, L. Mei, R. Li, Galerkin methods for the Davey–Stewartson equations, Applied Mathematics and Computation, 328 (2018), 144–161.

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

S. Tuluce Demiray, H. Bulut, New soliton solutions of Davey—Stewartson equation with power-law nonlinearity, Opt Quant. Electron., 49 (2017), 1– 8.

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

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

O.H. El-Kalaawy, R.S. Ibrahim, Solitary wave solution of the two-dimensional regularized longwave and Davey–Stewartson equations in fluids and plasmas, Appl. Math. Ser. B, 3 (8) (2012), 833–843.

G. Ebadi, E.V. Krishnan, M. Labidi, E.Zerrad, A. BiswasAnalytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity, Wave Random Complex, 21 (2011), 559–590.

J. Shi, J. Li, S. Li, Analytical travelling wave solutions and parameter analysis for the (2+1)-dimensional Davey–Stewartson-type equations, Pramana J. Phys., 81 (2013), 747–762.

V.A. Arkadiev, A.K. Pogrebkov, M.C.Polivanov, Inverse scattering transform method and soliton solutions for the Davey–Stewartson II equation, Phys. D, 36 (1989), 189–196.

X. Zhao, Self-similar solutions to a generalized Davey-Stewartson system, Math. Comput. Model., 50(9-10) (2009), 1394–1399.

Y. Ohta, J. Yang, Dynamics of rogue waves in the Davey–Stewartson II equation, J. Phys. A Math. Theor., 46 (10) (2013), 105202.

Y. Ohta, J. Yang, Rogue waves in the Davey–Stewartson I equation, Phys. Rev. A Math. Theor., 86 (2012), 036604.

D. Anker, N.C. Freeman, On the Solition Solutions of the Davey-Stewartson Equation for Long Waves, Proc. R. Soc. A., 360 (1978), 529–540.

B. Zhang, M.N. Xiong, L. Chen, Many New Exact Solutions for Generalized Davey-Stewartson Equation with Arbitrary Power Nonlinearities Using Novel (G0=G)-Expansion Method, Journal of Advances in Applied Mathematics, 4(1) (2019), 10–21.

M. Fazli Aghdaei, H. Adibi, New methods to solve the resonant nonlinear schrödinger equation with time-dependent coefficients, Optical and quantum electronics, 49 ( 2017), 316.

M. Song, Z.R. Liu, "Qualitative analysis and explicit traveling wave solutions for the Davey-Stewartson equation, Math methods appl sci, 37 (2014), 393–401.

J. Cao, H.Y. Lu, Exact traveling wave solutions of the generalized Davey-Stewartson equation, Journal of Shanghai normal university (natural sciences), 44 (2015), 330–338.

B. Ghanbari, M. Inc, A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation, Eur. Phys. J. Plus, 133 (2018), 142.

B. Ghanbari, J.F. Gomez-Aguilar, The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with b-conformable time derivative, Revista Mexicana de Fısica, 65(5) (2019), 503–518.

H.M. Srivastava, H. Günerhan, B. Ghanbari, Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity, Math Meth Appl Sci., (2019), 1–12.

B. Ghanbari,On novel non-differentiable exact solutions to local fractional Gardner’s equation using an effective technique, Math. Methods Appl. Sci. (2020), 1–13.

B. Ghanbari and A. Akgül,Abundant new analytical and approximate solutions to the generalized Schamelequation, Phys. Scr. 95 (2020), 075201.

B Ghanbari, M Inc, L Rada, Solitary wave solutions to the Tzitzeica type equations obtained by a new efficient approach, Journal of Applied Analysis and Computation 9 (2), (2018) 568-589.

B. Ghanbari, On the non-differentiable exact solutions to Schamel’s equation with local fractional derivative on Cantor sets, Numerical Methods for Partial Differential Equations, (2020) doi.org/10.1002/num.22740

B. Ghanbari, K. S. Nisar, and M. Aldhaifallah,Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method, Adv. Differ. Eq. 2020(2020), 1–25.

B. Ghanbari and N. Raza, An analytical method for soliton solutions of perturbed Schr¨dinger’s equation withquadratic-cubic nonlinearity, Mod. Phys. Lett. B 33 (2019), 1950018.

B. Ghanbari, A. Yusuf, and D. Baleanu,The new exact solitary wave solutions and stability analysis for the(2+1)-dimensional Zakharov–Kuznetsov equation, Adv. Differ. Eq. 2019 (2019), 1–15 18






07 Gravitation, Mathematical Physics and Field Theory