New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation

Ali Tozar

doi:10.32323/ujma.760899

EN

New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation

Abstract

In recent years, nonlinear concepts have attracted a lot of attention due to the deep mathematics and physics they contain. In explaining these concepts, nonlinear differential equations appear as an inevitable tool. In the past century, considerable efforts have been made and will continue to be made to solve many nonlinear differential equations. This study is also a step towards analytical solution of the complex Ginzburg-Landau equation (CGLE) used to describe many phenomena on a wide scale. In this study, the CGLE was solved analytically by $(1/G')$-expansion method.

Keywords

(1=G′)-Expansion Method, Complex Ginzburg-Landau Equation, Nonlinear Phenomena, Optical Solutions

References

[1] A.B. Abubakar, P. Kumam, A descent Dai-Liao conjugate gradient method for nonlinear equations, Numer. Algorithms, 81(1) (2019) 197-210.
[2] M.S. Gowda, D. Sossa, Weakly homogeneous variational inequalities and solvability of nonlinear equations over cones, Math. Program., 177(1-2) (2019) 149-171.
[3] R. Garra, E. Issoglio, G.S. Taverna, Fractional Brownian motions ruled by nonlinear equations, Appl. Math. Lett., 102 (2020) 106160.
[4] M.A. Al-Jawary, M.I. Adwan, G.H. Radhi, Three iterative methods for solving second order nonlinear ODEs arising in physics. J. King Saud Univ.-Sci., 32(1) (2020) 312-323.
[5] A.R. Seadawy, N. Cheemaa, Some new families of spiky solitary waves of one-dimensional higher-order K-dV equation with power law nonlinearity in plasma physics, Indian J. Phys., 94(1) (2020) 117-126.
[6] J.T. Kirby, A new instability for Boussinesq-type equations, J. Fluid Mech., (2020) 894.
[7] A. Tozar, O. Tasbozan, A. Kurt, Analytical solutions of Cahn-Hillard phase-field model for spinodal decomposition of a binary system. EPL (Europhysics Letters), 130(2) (2020) 24001.
[8] A. Esen, O. Tasbozan, Numerical solution of time fractional Schr¨odinger equation by using quadratic B-spline finite elements. In Annales Mathematicae Silesianae, 31 (2017) 83-98.
[9] O. Tasbozan, A. Kurt, A. Tozar, New optical solutions of complex Ginzburg-Landau equation arising in semiconductor lasers, Appl. Phys. B, 125(6) (2019) 104.
[10] A. Berti, V. Berti, A thermodynamically consistent Ginzburg-Landau model for superfluid transition in liquid helium, Z Angew. Math. Phys. 64 (2013) 1387-1397.

[11] R.J. Rivers, Zurek-Kibble causality bounds in time-dependent Ginzburg-Landau theory and quantum field theory, J. Low Temp. Phys. 124 (2001) 41-83.
[12] E. Kengne, A. Lakhssassi, R. Vaillancourt, et al., Exact solutions for generalized variable-coefficients Ginzburg-Landau equation: Application to Bose-Einstein condensates with multi-body interatomic interactions, J. Math. Phys. 53 (2012) 28.
[13] E. Atilgan, O. Tasbozan, A. Kurt, S.T. Mohyud-Din, Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic (CRWP) Equation and Modified Benjamin-Bona-Mahony (BBM) equation. Univ. J. Math. Appl., 3(2) (2020) 61-68.
[14] H. Yang, Homotopy analysis method for the time-fractional Boussinesq equation, Univ. J. Math. Appl., 3(1) (2020) 12-18.
[15] S. Toprakseven, The Existence and Uniqueness of Initial-Boundary Value Problems of the Fractional Caputo-Fabrizio Differential Equations. Univ. J. Math. Appl., 2(2) (2019) 100-106.
[16] A. Tozar, A. Kurt, O. Tasbozan, New wave solutions of time fractional integrable dispersive wave equation arising in ocean engineering models. Kuwait J. Sci., 47(2) (2020).
[17] A. Yokus, An expansion method for finding traveling wave solutions to nonlinear pdes, Istanbul Commerce Univ. J. Sci., 14 (2015) 65-81.
[18] H. Durur, A. Yokus, Hyperbolic Traveling Wave Solutions for Sawada.Kotera Equation Using (1=G0)-Expansion Method, AKU J. Sci. Eng., 19 (2019) 615-619.
[19] A. Yokus, H. Durur, Complex hyperbolic traveling wave solutions of Kuramoto-Sivashinsky equation using (1/G’) expansion method for nonlinear dynamic theory, J. BAUN Inst. Sci. Technol., 21 (2019) 590-599.
[20] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math, 264 (2014) 65-70.
[21] T. Abdeljawad, On conformable fractional calulus, J. Comput. Appl. Math. 279 (2015) 57-66.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Ali Tozar ^*
0000-0003-3039-1834
Türkiye

Publication Date

September 29, 2020

Submission Date

June 30, 2020

Acceptance Date

September 22, 2020

Published in Issue

Year 2020 Volume: 3 Number: 3

DOI

https://doi.org/10.32323/ujma.760899

IZ

https://izlik.org/JA54RB44JZ

APA

Tozar, A. (2020). New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Universal Journal of Mathematics and Applications, 3(3), 129-132. https://doi.org/10.32323/ujma.760899

AMA

1.Tozar A. New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Univ. J. Math. Appl. 2020;3(3):129-132. doi:10.32323/ujma.760899

Chicago

Tozar, Ali. 2020. “New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation”. Universal Journal of Mathematics and Applications 3 (3): 129-32. https://doi.org/10.32323/ujma.760899.

EndNote

Tozar A (September 1, 2020) New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Universal Journal of Mathematics and Applications 3 3 129–132.

IEEE

[1]A. Tozar, “New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation”, Univ. J. Math. Appl., vol. 3, no. 3, pp. 129–132, Sept. 2020, doi: 10.32323/ujma.760899.

ISNAD

Tozar, Ali. “New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation”. Universal Journal of Mathematics and Applications 3/3 (September 1, 2020): 129-132. https://doi.org/10.32323/ujma.760899.

JAMA

1.Tozar A. New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Univ. J. Math. Appl. 2020;3:129–132.

MLA

Tozar, Ali. “New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation”. Universal Journal of Mathematics and Applications, vol. 3, no. 3, Sept. 2020, pp. 129-32, doi:10.32323/ujma.760899.

Vancouver

1.Ali Tozar. New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Univ. J. Math. Appl. 2020 Sep. 1;3(3):129-32. doi:10.32323/ujma.760899