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Cogent Mathematics Volume 3, 2016 - Issue 1
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Research Article

Exact traveling wave solutions for the generalized Hirota-Satsuma couple KdV system using the exp(−φ(ξ))-expansion method

Mostafa M.A. KhaterFaculty of Science, Department of Mathematics, Mansoura University, 35516Mansoura, EgyptCorrespondence[email protected]
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Xiao-Jun YangChina unviersity of Mining and Technology, ChinaView further author information
(Reviewing Editor)
Article: 1172397 | Received 19 Jan 2016, Accepted 23 Mar 2016, Published online: 27 May 2016

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Mostafa M. A. Khater, Mustafa Inc, Raghda A. M. Attia, Dianchen Lu & Bandar Almohsen. (2020) Abundant new computational wave solutions of the GM-DP-CH equation via two modified recent computational schemes. Journal of Taibah University for Science 14:1, pages 1554-1562.
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Md. Habibul Bashar, Mustafa Inc, S.M. Rayhanul Islam, K.H. Mahmoud & M. Ali Akbar. (2022) Soliton solutions and fractional effects to the time-fractional modified equal width equation. Alexandria Engineering Journal 61:12, pages 12539-12547.
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S.M. Rayhanul Islam, Arzu Akbulut & S M Yiasir Arafat. (2022) Exact solutions of the different dimensional CBS equations in mathematical physics. Partial Differential Equations in Applied Mathematics 5, pages 100320.
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Jianmei Zhang, Dianchen Lu, Samir A. Salama & Mostafa M. A. Khater. (2022) Accurate demonstrating of the interactions of two long waves with different dispersion relations: Generalized Hirota–Satsuma couple KdV equation. AIP Advances 12:2.
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Lina Chang, Hanze Liu, Xuexia Li & Xiangpeng Xin. (2021) Equivalence Transformation, Dynamical Analysis and Exact Solutions of Harry-Dym System with Variable Coefficients. Qualitative Theory of Dynamical Systems 20:2.
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Yu-Ming Chu, Muhannad A. Shallal, Seyed Mehdi Mirhosseini-Alizamini, Hadi Rezazadeh, Shumaila Javeed & Dumitru Baleanu. (2021) Application of Modified Extended Tanh Technique for solving Complex Ginzburg-Landau Equation considering Kerr Law Nonlinearity. Computers, Materials & Continua 66:2, pages 1369-1378.
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Seyed Mehdi Mirhosseini-Alizamini, Hadi Rezazadeh, Kumbinarasaiah Srinivasa & Ahmet Bekir. (2020) New closed form solutions of the new coupled Konno–Oono equation using the new extended direct algebraic method. Pramana 94:1.
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Mostafa M. A. Khater, Choonkil Park & Dianchen Lu. (2020) Two effective computational schemes for a prototype of an excitable system. AIP Advances 10:10, pages 105120.
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Mostafa M. A. Khater, Raghda A. M. Attia, Sultan S. Alodhaibi & Dianchen Lu. (2020) Novel soliton waves of two fluid nonlinear evolutions models in the view of computational scheme. International Journal of Modern Physics B 34:10, pages 2050096.
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Lina Chang, Hanze Liu & Lijun Zhang. (2020) Symmetry Reductions, Dynamical Behavior and Exact Explicit Solutions to a Class of Nonlinear Shallow Water Wave Equation. Qualitative Theory of Dynamical Systems 19:1.
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Ahmad T. Ali, Mostafa M.A. Khater, Raghda A.M. Attia, Abdel-Haleem Abdel-Aty & Dianchen Lu. (2020) Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system. Chaos, Solitons & Fractals 131, pages 109473.
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M Ali Akbar, Norhashidah Hj Mohd Ali & Tasnim Tanjim. (2019) Outset of multiple soliton solutions to the nonlinear Schrödinger equation and the coupled Burgers equation. Journal of Physics Communications 3:9, pages 095013.
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G. Yel, H. M. Baskonus & H. Bulut. (2018) Regarding some novel exponential travelling wave solutions to the Wu–Zhang system arising in nonlinear water wave model. Indian Journal of Physics 93:8, pages 1031-1039.
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Raghda Attia, Dianchen Lu & Mostafa M. A. Khater. (2019) Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation. Mathematical and Computational Applications 24:1, pages 10.
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Hong-Zhun Liu. (2018) An equivalent form for the $$\exp (-\phi (\xi ))$$ exp ( - ϕ ( ξ ) ) -expansion method. Japan Journal of Industrial and Applied Mathematics 35:3, pages 1153-1161.
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Mostafa M. A. Khater & Dipankar Kumar. (2017) Implementation of three reliable methods for finding the exact solutions of (2 + 1) dimensional generalized fractional evolution equations. Optical and Quantum Electronics 50:11.
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Tarikul Islam, M. Ali Akbar & Abul Kalam Azad. (2018) Traveling wave solutions to some nonlinear fractional partial differential equations through the rational ( G ′/ G )-expansion method. Journal of Ocean Engineering and Science 3:1, pages 76-81.
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Mostafa M.A. Khater, Aly R. Seadawy & Dianchen Lu. (2018) Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method. Superlattices and Microstructures 113, pages 346-358.
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Kamran Ayub, M. Yaqub Khan & Qazi Mahmood-Ul-Hassan. (2017) Solitary and periodic wave solutions of Calogero–Bogoyavlenskii–Schiff equation via exp-function methods. Computers & Mathematics with Applications 74:12, pages 3231-3241.
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Dianchen Lu, Aly R. Seadawy & Mostafa M.A. Khater. (2017) Bifurcations of new multi soliton solutions of the van der Waals normal form for fluidized granular matter via six different methods. Results in Physics 7, pages 2028-2035.
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