Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2020, Cilt: 3 Sayı: 3, 129 - 132, 29.09.2020

Ali Tozar

https://doi.org/10.32323/ujma.760899
Cited By: 5

Öz

Kaynakça

  • [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.

New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation

Yıl 2020, Cilt: 3 Sayı: 3, 129 - 132, 29.09.2020

Ali Tozar

https://doi.org/10.32323/ujma.760899
Cited By: 5

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ali Tozar 0000-0003-3039-1834

Yayımlanma Tarihi 29 Eylül 2020
Gönderilme Tarihi 30 Haziran 2020
Kabul Tarihi 22 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 3

Kaynak Göster

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 Tozar A. New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Univ. J. Math. Appl. Eylül 2020;3(3):129-132. doi:10.32323/ujma.760899
Chicago Tozar, Ali. “New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation”. Universal Journal of Mathematics and Applications 3, sy. 3 (Eylül 2020): 129-32. https://doi.org/10.32323/ujma.760899.
EndNote Tozar A (01 Eylül 2020) New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Universal Journal of Mathematics and Applications 3 3 129–132.
IEEE A. Tozar, “New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation”, Univ. J. Math. Appl., c. 3, sy. 3, ss. 129–132, 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 (Eylül 2020), 129-132. https://doi.org/10.32323/ujma.760899.
JAMA 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, c. 3, sy. 3, 2020, ss. 129-32, doi:10.32323/ujma.760899.
Vancouver Tozar A. New Analytical Solutions of Fractional Complex Ginzburg-Landau Equation. Univ. J. Math. Appl. 2020;3(3):129-32.

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 Kapak Resmi İndir

 23181

Universal Journal of Mathematics and Applications 

29207              

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