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International Journal of Computer Mathematics Volume 72, 1999 - Issue 4
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Original Articles

On the solution of a korteweg-de vries like equation by the decomposition method

D. Kaya Department of Mathematics, Firat University, Elazig, 23119, Turkey
Pages 531-539 | Received 25 Mar 1998, Published online: 19 Mar 2007

Citations (61)

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Jun Wang, Khurrem Shehzad, Aly R. Seadawy, Muhammad Arshad & Farwa Asmat. (2023) Dynamic study of multi-peak solitons and other wave solutions of new coupled KdV and new coupled Zakharov–Kuznetsov systems with their stability. Journal of Taibah University for Science 17:1.
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Syed Tauseef Mohyud-Din, Muhammad Aslam Noor & Farah Jabeen. (2011) Modified Variational Iteration Method for Traveling Wave Solutions of Seventh-order Generalized KdV Equations. International Journal for Computational Methods in Engineering Science and Mechanics 12:3, pages 107-113.
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Articles from other publishers (59)

Maria Ihsane El Bahi & Khalid Hilal. (2022) Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation. Advances in Mathematical Physics 2022, pages 1-11.
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Ali Başhan. (2021) Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments. Applied Numerical Mathematics 167, pages 356-374.
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Maria Ihsane El Bahi & Khalid Hilal. (2021) Lie Symmetry Analysis, Exact Solutions, and Conservation Laws for the Generalized Time-Fractional KdV-Like Equation. Journal of Function Spaces 2021, pages 1-10.
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Necdet Bildik. (2019) On the Solution of KdV-Like Equations by the Optimal Perturbation Iteration Technique. International Journal of Applied Physics and Mathematics 9:1, pages 29-37.
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Talat Sultana, Arshad Khan & Pooja Khandelwal. (2018) A new non-polynomial spline method for solution of linear and non-linear third order dispersive equations. Advances in Difference Equations 2018:1.
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H.O. Bakodah, N.A. Al-Zaid, Mohammad Mirzazadeh & Qin Zhou. (2017) Decomposition method for Solving Burgers’ Equation with Dirichlet and Neumann boundary conditions. Optik 130, pages 1339-1346.
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M MATINFAR, M ESLAMI & M KORDY. (2015) The functional variable method for solving the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations. Pramana 85:4, pages 583-592.
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Syed Tauseef Mohyud‐Din, Ahmet Yıldırım & Eda Yülüklü. (2012) Homotopy analysis method for space‐ and time‐fractional KdV equation. International Journal of Numerical Methods for Heat & Fluid Flow 22:7, pages 928-941.
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Syed Tauseef Mohyud-Din, Ahmet Yildirim & M. M. Hosseini. (2010) Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials. International Journal of Differential Equations 2010, pages 1-28.
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SYED TAUSEEF MOHYUD-DIN, MUHAMMAD ASLAM NOOR & KHALIDA INAYAT NOOR. (2012) TRAVELING WAVE SOLUTIONS OF SEVENTH-ORDER GENERALIZED KdV EQUATIONS BY VARIATIONAL ITERATION METHOD USING ADOMIAN'S POLYNOMIALS. International Journal of Modern Physics B 23:15, pages 3265-3277.
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Syed Tauseef Mohyud-Din, Muhammad Aslam Noor & Khalida Inayat Noor. (2009) Some Relatively New Techniques for Nonlinear Problems. Mathematical Problems in Engineering 2009, pages 1-25.
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Yavuz Ugurlu & Dogan Kaya. (2008) Exact and numerical solutions of generalized Drinfeld–Sokolov equations. Physics Letters A 372:16, pages 2867-2873.
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Shaher Momani, Zaid Odibat & Ahmed Alawneh. (2008) Variational iteration method for solving the space- and time-fractional KdV equation. Numerical Methods for Partial Differential Equations 24:1, pages 262-271.
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Ibrahim E. Inan. (2007) Exact solutions for coupled KdV equation and KdV equations. Physics Letters A 371:1-2, pages 90-95.
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Mário Basto, Viriato Semiao & Francisco L. Calheiros. (2007) Numerical study of modified Adomian's method applied to Burgers equation. Journal of Computational and Applied Mathematics 206:2, pages 927-949.
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D. Lesnic. (2007) A reliable technique for solving third‐order dispersion equations. Kybernetes 36:5/6, pages 697-708.
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Doǧan Kaya & Kamel Al-Khaled. (2007) A numerical comparison of a Kawahara equation. Physics Letters A 363:5-6, pages 433-439.
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Jie-min Zhan & Yok-sheung Li. (2006) Generalized finite spectral method for 1D Burgers and KdV equations. Applied Mathematics and Mechanics 27:12, pages 1635-1643.
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S.A. El-Wakil, A. Elhanbaly & M.A. Abdou. (2006) Adomian decomposition method for solving fractional nonlinear differential equations. Applied Mathematics and Computation 182:1, pages 313-324.
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A. Elhanbaly & M.A. Abdou. (2006) New application of Adomian decomposition method on Fokker–Planck equation. Applied Mathematics and Computation 182:1, pages 301-312.
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Necat Polat, Dogˇan Kaya & H. Ilhan Tutalar. (2006) A analytic and numerical solution to a modified Kawahara equation and a convergence analysis of the method. Applied Mathematics and Computation 181:1, pages 193-199.
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Necat Polat, Dogˇan Kaya & H. Ilhan Tutalar. (2006) A analytic and numerical solution to a modified Kawahara equation and a convergence analysis of the method. Applied Mathematics and Computation 179:2, pages 466-472.
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M A Abdou & A Elhanbaly. (2006) Decomposition method for solving a system of coupled fractional-time nonlinear equations. Physica Scripta 73:4, pages 338-348.
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D. Lesnic. (2006) The decomposition method for linear, one-dimensional, time-dependent partial differential equations. International Journal of Mathematics and Mathematical Sciences 2006, pages 1-29.
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Doğan Kaya. (2006) The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation. Physics Letters A 348:3-6, pages 244-250.
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Salah M. El-Sayed & Dogˇan Kaya. (2006) A numerical solution and an exact explicit solution of the NLS equation. Applied Mathematics and Computation 172:2, pages 1315-1322.
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Turabi Geyikli & Dogˇan Kaya. (2005) An application for a modified KdV equation by the decomposition method and finite element method. Applied Mathematics and Computation 169:2, pages 971-981.
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Turabi Geyikli & Dogˇan Kaya. (2005) Comparison of the solutions obtained by B-spline FEM and ADM of KdV equation. Applied Mathematics and Computation 169:1, pages 146-156.
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Shaher Momani. (2005) An explicit and numerical solutions of the fractional KdV equation. Mathematics and Computers in Simulation 70:2, pages 110-118.
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Doǧan Kaya. (2005) An application for the higher order modified KdV equation by decomposition method. Communications in Nonlinear Science and Numerical Simulation 10:6, pages 693-702.
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Dogˇan Kaya & Ibrahim E. Inan. (2005) A numerical application of the decomposition method for the combined KdV–MKdV equation. Applied Mathematics and Computation 168:2, pages 915-926.
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Salah M. El-Sayed & Dogˇan Kaya. (2005) Exact and numerical traveling wave solutions of Whitham–Broer–Kaup equations. Applied Mathematics and Computation 167:2, pages 1339-1349.
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Dogˇan Kaya. (2005) An implementation of the ADM for generalized one-dimensional Klein-Gordon equation. Applied Mathematics and Computation 166:2, pages 426-433.
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Dogˇan Kaya. (2005) On experimental results and explicit exact solutions for the generalized Boussinesq type equation. Applied Mathematics and Computation 165:2, pages 303-311.
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Dogˇan Kaya & Asif Yokus. (2005) A decomposition method for finding solitary and periodic solutions for a coupled higher-dimensional Burgers equations. Applied Mathematics and Computation 164:3, pages 857-864.
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Doǧan Kaya & Ibrahim E. Inan. (2005) A convergence analysis of the ADM and an application. Applied Mathematics and Computation 161:3, pages 1015-1025.
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D. Kaya. (2004) An application of the decompositionmethod for the two-dimensional KdV-Burgers equation. Computers & Mathematics with Applications 48:10-11, pages 1659-1665.
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Doǧan Kaya. (2004) An application of the modified decomposition method for two dimensional sine-Gordon equation. Applied Mathematics and Computation 159:1, pages 1-9.
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Kamel Al-Khaled, Dogan Kaya & Muhammad Aslam Noor. (2004) Numerical comparison of methods for solving parabolic equations. Applied Mathematics and Computation 157:3, pages 735-743.
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Salah M. El-Sayed & Doǧan Kaya. (2004) On the numerical solution of the system of two-dimensional Burgers' equations by the decomposition method. Applied Mathematics and Computation 158:1, pages 101-109.
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Salah M. El-Sayed & Doǧan Kaya. (2004) The decomposition method for solving (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation. Applied Mathematics and Computation 157:2, pages 523-534.
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Salah M. El-Sayed & Doǧan Kaya. (2004) An application of the ADM to seven-order Sawada–Kotara equations. Applied Mathematics and Computation 157:1, pages 93-101.
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Doǧan Kaya. (2004) A reliable method for the numerical solution of the kinetics problems. Applied Mathematics and Computation 156:1, pages 261-270.
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Doğan Kaya & Salah M. El-Sayed. (2004) Adomian's decomposition method applied to systems of nonlinear algebraic equations. Applied Mathematics and Computation 154:2, pages 487-493.
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N. Shawagfeh & D. Kaya. (2004) Series solution to the Pochhammer-Chreeequation and comparison with exact solutions. Computers & Mathematics with Applications 47:12, pages 1915-1920.
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Doǧan Kaya. (2004) Solitary-wave solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. Applied Mathematics and Computation 152:3, pages 709-720.
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Doǧan Kaya. (2004) Exact and numerical soliton solutions of some nonlinear physical models. Applied Mathematics and Computation 152:2, pages 551-560.
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Doǧan Kaya & Salah M. El-Sayed. (2004) A numerical simulation and explicit solutions of the generalized Burgers–Fisher equation. Applied Mathematics and Computation 152:2, pages 403-413.
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Doǧan Kaya. (2004) An application of the decomposition method for the KdVB equation. Applied Mathematics and Computation 152:1, pages 279-288.
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Doǧan Kaya & Ibrahim E Inan. (2004) Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation. Applied Mathematics and Computation 151:3, pages 775-787.
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N Shawagfeh & D Kaya. (2004) Comparing numerical methods for the solutions of systems of ordinary differential equations. Applied Mathematics Letters 17:3, pages 323-328.
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Salah M. El-Sayed & Doǧan Kaya. (2004) Comparing numerical methods for Helmholtz equation model problem. Applied Mathematics and Computation 150:3, pages 763-773.
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Doǧan Kaya. (2004) A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation. Applied Mathematics and Computation 149:3, pages 833-841.
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Doǧan Kaya. (2004) Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation. Applied Mathematics and Computation 147:1, pages 69-78.
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Doǧan Kaya & Salah M. El-Sayed. (2003) Numerical soliton-like solutions of the potential Kadomtsev–Petviashvili equation by the decomposition method. Physics Letters A 320:2-3, pages 192-199.
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Doǧan Kaya & Salah M. El-Sayed. (2003) A numerical method for solving Jaulent–Miodek equation. Physics Letters A 318:4-5, pages 345-353.
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Doǧan Kaya & Salah M. El-Sayed. (2003) On the solution of the coupled Schrödinger–KdV equation by the decomposition method. Physics Letters A 313:1-2, pages 82-88.
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Doǧan Kaya & Salah M. El-Sayed. (2003) On a generalized fifth order KdV equations. Physics Letters A 310:1, pages 44-51.
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Dogan Kaya & Mohammed Aassila. (2002) An application for a generalized KdV equation by the decomposition method. Physics Letters A 299:2-3, pages 201-206.
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