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Year 2021, Volume: 42 Issue: 1, 88 - 98, 29.03.2021

Asıf Yokuş , Hülya Durur

https://doi.org/10.17776/csj.689759
Cited By: 6

Abstract

Supporting Institution

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References

  • [1] Ekici M., Mirzazadeh M., Sonmezoglu A., Ullah M. Z., Zhou Q., Triki H., Biswas A., Optical solitons with anti-cubic nonlinearity by extended trial equation method, Optik, 136 (2017) 368-373.
  • [2] Rezazadeh H., Tariq H., Eslami M., Mirzazadeh M., Zhou Q., New exact solutions of nonlinear conformable time-fractional Phi-4 equation, Chinese Journal of Physics, 56 (6) (2018) 2805-2816.
  • [3] Durur H., Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method, Modern Physics Letters B, 34(03) (2020) 2050036.
  • [4] Yokus A., Kuzu B., Demiroğlu U., Investigation of solitary wave solutions for the (3+1)-dimensional Zakharov - Kuznetsov equation. International Journal of Modern Physics B, 33(29) (2019) 1950350.
  • [5] Su-Ping Q., Li-Xin T., Modification of the Clarkson–Kruskal Direct Method for a Coupled System, Chinese Physics Letters, 24 (10) (2007) 2720. [6] Manafian J., Lakestani, M., Abundant soliton solutions for the Kundu–Eckhaus equation via tan (ϕ (ξ))-expansion method, Optik, 127 (14) (2016) 5543-5551.
  • [7] Yavuz M., Özdemir N., An Integral Transform Solution for Fractional Advection-Diffusion Problem, Mathematical Studies and Applications, 442 (2018) 4-6 October.
  • [8] Duran S., Kaya D., Applications of a new expansion method for finding wave solutions of nonlinear differential equations, World Applied Sciences Journal, 18 (11) (2012) 1582-1592. [9] Cattani C., Sulaiman T. A., Baskonus H. M., Bulut H., On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel’d-Sokolov systems, Optical and Quantum Electronics, 50 (3) (2018) 138.
  • [10] Kumar D., Seadawy A. R., Joardar A. K., Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chinese journal of physics, 56 (1) (2018) 75-85.
  • [11] Yokuş A., Durur H., Complex hyperbolic traveling wave solutions of Kuramoto-Sivashinsky equation using (1/G') expansion method for nonlinear dynamic theory, Journal of Balıkesir University Institute of Science and Technology, 21 (2) (2019) 590-599.
  • [12] Yokus A., Durur H., Ahmad H., Thounthong, P., Zhang Y. F., Construction of exact traveling wave solutions of the Bogoyavlenskii equation by (G′/G,1/G)-expansion and (1/G′)-expansion techniques, Results in Physics, 19 (2020) 103409.
  • [13] Yokus A., Durur H., Ahmad H., Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system, Facta Universitatis, Series: Mathematics and Informatics, 35 (2) (2020) 523-531.
  • [14] Durur H., Yokuş A., Analytical solutions of Kolmogorov–Petrovskii–Piskunov equation, Journal of Balikesir University Institute of Science and Technology, 22 (2) (2020) 628-636.
  • [15] Yokus A., Durur H., Ahmad H., Yao S. W., Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation, Mathematics, 8 (6) (2020) 908.
  • [16] Aziz I., Šarler, B., The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets, Mathematical and Computer Modelling, 52 (9-10) (2010) 1577-1590.
  • [17] Aziz I., Asif M., Haar wavelet collocation method for three-dimensional elliptic partial differential equations, Computers & Mathematics with Applications, 73 (9) (2017) 2023-2034.
  • [18] Darvishi M., Arbabi S., Najafi M., Wazwaz, A., Traveling wave solutions of a (2+1)-dimensional Zakharov-like equation by the first integral method and the tanh method, Optik, 127 (16) (2016) 6312-6321.
  • [19] Gao W., Silambarasan R., Baskonus H. M., Anand R. V. and Rezazadeh H., Periodic waves of the non-dissipative double dispersive micro strain wave in the micro structured solids, Physica A: Statistical Mechanics and its Applications, 545 (2020).
  • [20] Duran S., Askin M., Sulaiman T. A., New soliton properties to the ill-posed Boussinesq equation arising in nonlinear physical science, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7 (3) (2017) 240-247.
  • [21] Faraj B., Modanli M., Using Difference Scheme Method for the Numerical Solution of Telegraph Partial Differential Equation, (2017).
  • [22] Çelik N., Seadawy A. R., Özkan Y. S., Yaşar E., A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws, Chaos, Solitons & Fractals, 143 (2021) 110486.
  • [23] Duran S., Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G'/G, 1/G)-Expansion Method, Adıyaman University Journal of Science, 10 (2) (2020) 585-594.
  • [24] Yavuz M., Sulaiman T. A., Yusuf A., Abdeljawad T., The Schrödinger-KdV equation of fractional order with Mittag-Leffler nonsingular kernel. Alexandria Engineering Journal, 60(2) (2021) 2715-2724.
  • [25] Evirgen F., Uçar S., Özdemir N., Hammouch Z., System response of an alcoholism model under the effect of immigration via non-singular kernel derivative, Discrete and Continuous Dynamical Systems-S, (2018) 10.
  • [26] Kaya D., Bulut H., Inc, M., Numerical Study of a Klein-Gordon Equation by The Adomian's Decompositon Method, Hadronic Journal, 28 (3) (2005) 311.
  • [27] Duran S., Exact Solutions for Time-Fractional Ramani and Jimbo-Miwa Equations by Direct Algebraic Method, Advanced Science, Engineering and Medicine, 12 (7) (2020) 982-988.
  • [28] Yokuş A., Durur H., Abro K. A., Kaya D., Role of Gilson–Pickering equation for the different types of soliton solutions: a nonlinear analysis, The European Physical Journal Plus, 135 (8) (2020) 1-19.
  • [29] Duran S., Kaya D., New Wave Solutions for Nonlinear Differential Equations using an Extended Bernoulli Equation as a New Expansion Method, In ITM Web of Conferences, Kıbrıs-Girne, (2018), (22) 01035 1-5.
  • [30] Siddique I., Rizvi, S. T. R., Batool, F., New exact travelling wave solutions of nonlinear evolution equations, International Journal of Nonlinear Science, 9 (1) (2010) 12-18.
  • [31] Jimbo M., Miwa T., Solitons and infinite dimensional Lie algebras, Publications of the Research Institute for Mathematical Sciences, 19 (3) (1983) 943-1001.
  • [32] Wazwaz A. M., Multiple-soliton solutions for extended (3+1)-dimensional Jimbo–Miwa equations, Applied Mathematics Letters, 64 (2017) 21-26.
  • [33] Zhang S., New periodic wave solutions of a (3+1)-dimensional Jimbo–Miwa equation. SN Applied Sciences, 1 (3) (2019) 201.
  • [34] Ma W. X., Lee J. H., A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation, Chaos, Solitons & Fractals, 42 (3) (2009) 1356-1363.
  • [35] Sun H. Q., Chen, A. H., Lump and lump–kink solutions of the (3+1)-dimensional Jimbo–Miwa and two extended Jimbo–Miwa equations, Applied Mathematics Letters, 68 (2017) 55-61.
  • [36] Yang J. Y., Ma W. X., Abundant lump-type solutions of the Jimbo–Miwa equation in (3+1)-dimensions, Computers & Mathematics with Applications, 73 (2) (2017) 220-225.
  • [37] Liu X. Q., Jiang S., New solutions of the 3+1 dimensional Jimbo–Miwa equation. Applied mathematics and computation, 158 (1) (2004) 177-184.
  • [38] Öziş T., Aslan İ., Exact and explicit solutions to the (3+ 1)-dimensional Jimbo–Miwa equation via the Exp-function method, Physics Letters A, 372 (47) (2008) 7011-7015.
  • [39] Tang X. Y., Liang Z. F., Variable separation solutions for the (3+1)-dimensional Jimbo–Miwa equation, Physics Letters A, 351 (6) (2006) 398-402.
  • [40] Ma W. X., Lump-type solutions to the (3+1)-dimensional Jimbo-Miwa equation, International Journal of Nonlinear Sciences and Numerical Simulation, 17 (7-8) (2016) 355-359.

(G'/G,1/G)-expansion method for analytical solutions of Jimbo-Miwa equation

Year 2021, Volume: 42 Issue: 1, 88 - 98, 29.03.2021

Asıf Yokuş , Hülya Durur

https://doi.org/10.17776/csj.689759
Cited By: 6

Abstract

The main goal of this study is obtaining analytical solutions for (3+1)-dimensional Jimbo-Miwa Equation which the second equation in the well-known KP hierarchy of integrable systems. For the (3+1DJM) equation, hyperbolic, trigonometric, complex trigonometric and rational traveling wave solutions have been constructed by applying the (G'/G,1/G)-expansion method. Then, real and imaginary graphics are presented by giving special values to the constants in the solutions obtained. These graphics are a special solution of the (3+1DJM) equation and represent a stationary wave of the equation. The (G'/G,1/G)-expansion method is an effective and powerful method for solving nonlinear evolution equations (NLEEs). Ready computer package program is used to obtain the solutions and graphics presented in this study. 

Keywords

(3+1)-dimensional Jimbo-Miwa equation exact solution (G'/G-1/G)-expansion method traveling wave solution

References

  • [1] Ekici M., Mirzazadeh M., Sonmezoglu A., Ullah M. Z., Zhou Q., Triki H., Biswas A., Optical solitons with anti-cubic nonlinearity by extended trial equation method, Optik, 136 (2017) 368-373.
  • [2] Rezazadeh H., Tariq H., Eslami M., Mirzazadeh M., Zhou Q., New exact solutions of nonlinear conformable time-fractional Phi-4 equation, Chinese Journal of Physics, 56 (6) (2018) 2805-2816.
  • [3] Durur H., Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method, Modern Physics Letters B, 34(03) (2020) 2050036.
  • [4] Yokus A., Kuzu B., Demiroğlu U., Investigation of solitary wave solutions for the (3+1)-dimensional Zakharov - Kuznetsov equation. International Journal of Modern Physics B, 33(29) (2019) 1950350.
  • [5] Su-Ping Q., Li-Xin T., Modification of the Clarkson–Kruskal Direct Method for a Coupled System, Chinese Physics Letters, 24 (10) (2007) 2720. [6] Manafian J., Lakestani, M., Abundant soliton solutions for the Kundu–Eckhaus equation via tan (ϕ (ξ))-expansion method, Optik, 127 (14) (2016) 5543-5551.
  • [7] Yavuz M., Özdemir N., An Integral Transform Solution for Fractional Advection-Diffusion Problem, Mathematical Studies and Applications, 442 (2018) 4-6 October.
  • [8] Duran S., Kaya D., Applications of a new expansion method for finding wave solutions of nonlinear differential equations, World Applied Sciences Journal, 18 (11) (2012) 1582-1592. [9] Cattani C., Sulaiman T. A., Baskonus H. M., Bulut H., On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel’d-Sokolov systems, Optical and Quantum Electronics, 50 (3) (2018) 138.
  • [10] Kumar D., Seadawy A. R., Joardar A. K., Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chinese journal of physics, 56 (1) (2018) 75-85.
  • [11] Yokuş A., Durur H., Complex hyperbolic traveling wave solutions of Kuramoto-Sivashinsky equation using (1/G') expansion method for nonlinear dynamic theory, Journal of Balıkesir University Institute of Science and Technology, 21 (2) (2019) 590-599.
  • [12] Yokus A., Durur H., Ahmad H., Thounthong, P., Zhang Y. F., Construction of exact traveling wave solutions of the Bogoyavlenskii equation by (G′/G,1/G)-expansion and (1/G′)-expansion techniques, Results in Physics, 19 (2020) 103409.
  • [13] Yokus A., Durur H., Ahmad H., Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system, Facta Universitatis, Series: Mathematics and Informatics, 35 (2) (2020) 523-531.
  • [14] Durur H., Yokuş A., Analytical solutions of Kolmogorov–Petrovskii–Piskunov equation, Journal of Balikesir University Institute of Science and Technology, 22 (2) (2020) 628-636.
  • [15] Yokus A., Durur H., Ahmad H., Yao S. W., Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation, Mathematics, 8 (6) (2020) 908.
  • [16] Aziz I., Šarler, B., The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets, Mathematical and Computer Modelling, 52 (9-10) (2010) 1577-1590.
  • [17] Aziz I., Asif M., Haar wavelet collocation method for three-dimensional elliptic partial differential equations, Computers & Mathematics with Applications, 73 (9) (2017) 2023-2034.
  • [18] Darvishi M., Arbabi S., Najafi M., Wazwaz, A., Traveling wave solutions of a (2+1)-dimensional Zakharov-like equation by the first integral method and the tanh method, Optik, 127 (16) (2016) 6312-6321.
  • [19] Gao W., Silambarasan R., Baskonus H. M., Anand R. V. and Rezazadeh H., Periodic waves of the non-dissipative double dispersive micro strain wave in the micro structured solids, Physica A: Statistical Mechanics and its Applications, 545 (2020).
  • [20] Duran S., Askin M., Sulaiman T. A., New soliton properties to the ill-posed Boussinesq equation arising in nonlinear physical science, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7 (3) (2017) 240-247.
  • [21] Faraj B., Modanli M., Using Difference Scheme Method for the Numerical Solution of Telegraph Partial Differential Equation, (2017).
  • [22] Çelik N., Seadawy A. R., Özkan Y. S., Yaşar E., A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws, Chaos, Solitons & Fractals, 143 (2021) 110486.
  • [23] Duran S., Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G'/G, 1/G)-Expansion Method, Adıyaman University Journal of Science, 10 (2) (2020) 585-594.
  • [24] Yavuz M., Sulaiman T. A., Yusuf A., Abdeljawad T., The Schrödinger-KdV equation of fractional order with Mittag-Leffler nonsingular kernel. Alexandria Engineering Journal, 60(2) (2021) 2715-2724.
  • [25] Evirgen F., Uçar S., Özdemir N., Hammouch Z., System response of an alcoholism model under the effect of immigration via non-singular kernel derivative, Discrete and Continuous Dynamical Systems-S, (2018) 10.
  • [26] Kaya D., Bulut H., Inc, M., Numerical Study of a Klein-Gordon Equation by The Adomian's Decompositon Method, Hadronic Journal, 28 (3) (2005) 311.
  • [27] Duran S., Exact Solutions for Time-Fractional Ramani and Jimbo-Miwa Equations by Direct Algebraic Method, Advanced Science, Engineering and Medicine, 12 (7) (2020) 982-988.
  • [28] Yokuş A., Durur H., Abro K. A., Kaya D., Role of Gilson–Pickering equation for the different types of soliton solutions: a nonlinear analysis, The European Physical Journal Plus, 135 (8) (2020) 1-19.
  • [29] Duran S., Kaya D., New Wave Solutions for Nonlinear Differential Equations using an Extended Bernoulli Equation as a New Expansion Method, In ITM Web of Conferences, Kıbrıs-Girne, (2018), (22) 01035 1-5.
  • [30] Siddique I., Rizvi, S. T. R., Batool, F., New exact travelling wave solutions of nonlinear evolution equations, International Journal of Nonlinear Science, 9 (1) (2010) 12-18.
  • [31] Jimbo M., Miwa T., Solitons and infinite dimensional Lie algebras, Publications of the Research Institute for Mathematical Sciences, 19 (3) (1983) 943-1001.
  • [32] Wazwaz A. M., Multiple-soliton solutions for extended (3+1)-dimensional Jimbo–Miwa equations, Applied Mathematics Letters, 64 (2017) 21-26.
  • [33] Zhang S., New periodic wave solutions of a (3+1)-dimensional Jimbo–Miwa equation. SN Applied Sciences, 1 (3) (2019) 201.
  • [34] Ma W. X., Lee J. H., A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation, Chaos, Solitons & Fractals, 42 (3) (2009) 1356-1363.
  • [35] Sun H. Q., Chen, A. H., Lump and lump–kink solutions of the (3+1)-dimensional Jimbo–Miwa and two extended Jimbo–Miwa equations, Applied Mathematics Letters, 68 (2017) 55-61.
  • [36] Yang J. Y., Ma W. X., Abundant lump-type solutions of the Jimbo–Miwa equation in (3+1)-dimensions, Computers & Mathematics with Applications, 73 (2) (2017) 220-225.
  • [37] Liu X. Q., Jiang S., New solutions of the 3+1 dimensional Jimbo–Miwa equation. Applied mathematics and computation, 158 (1) (2004) 177-184.
  • [38] Öziş T., Aslan İ., Exact and explicit solutions to the (3+ 1)-dimensional Jimbo–Miwa equation via the Exp-function method, Physics Letters A, 372 (47) (2008) 7011-7015.
  • [39] Tang X. Y., Liang Z. F., Variable separation solutions for the (3+1)-dimensional Jimbo–Miwa equation, Physics Letters A, 351 (6) (2006) 398-402.
  • [40] Ma W. X., Lump-type solutions to the (3+1)-dimensional Jimbo-Miwa equation, International Journal of Nonlinear Sciences and Numerical Simulation, 17 (7-8) (2016) 355-359.
There are 38 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Asıf Yokuş 0000-0002-1460-8573

Hülya Durur 0000-0002-9297-6873

Publication Date March 29, 2021
Submission Date February 15, 2020
Acceptance Date December 23, 2020
Published in Issue Year 2021Volume: 42 Issue: 1

Cite

APA Yokuş, A., & Durur, H. (2021). (G’/G,1/G)-expansion method for analytical solutions of Jimbo-Miwa equation. Cumhuriyet Science Journal, 42(1), 88-98. https://doi.org/10.17776/csj.689759

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