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Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2017 / Cilt: 13 - Sayı: 3

Symmetry Reductions, Exact Solutions and Conservation Laws for the Coupled Nonlinear Klein-Gordon System

Emrullah YAŞAR
İlker Burak GİRESUNLU
Pages
593–599
Publication Date
2017-09-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition, by using the multiplier method, we derive the local conservation laws of the coupled nonlinear Klein-Gordon system.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The Lie group method is applied to a coupled nonlinear Klein-Gordon system.
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Key Findings & Data:The Klein-Gordon system is used to model many nonlinear phenomena including the propagation of dislocations in crystals and the behavior of elementary particles and the propagation of fluxons in Josephson junctions.
💡
Conclusion & Impact:In addition, by using the multiplier method, we derive the local conservation laws of the coupled nonlinear Klein-Gordon system.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Lie symmetry analysis · Coupled nonlinear Klein-Gordon system · Similarity reduction

Abstract

The Lie group method is applied to a coupled nonlinear Klein-Gordon system. The Klein-Gordon system is used to model many nonlinear phenomena including the propagation of dislocations in crystals and the behavior of elementary particles and the propagation of fluxons in Josephson junctions. The symmetry reductions and exact solutions which include the stationary and solitary waves are obtained. In addition, by using the multiplier method, we derive the local conservation laws of the coupled nonlinear Klein-Gordon system.

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Cite This Article

YAŞAR, E., GİRESUNLU, İ. B. (2017). Symmetry Reductions, Exact Solutions and Conservation Laws for the Coupled Nonlinear Klein-Gordon System. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 13 - Sayı: 3, 593–599. https://ajindex.com/articles/114349

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References (15)

  1. Vakhnenko, V.O, Parkes, E.J, Morrison, A.J, A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos, Soliton and Fractals. 2003, 17, 683-92.
  2. Hirota, R, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Physical Review Letters. 1971, 27, 1192-1195.
  3. Ma, Y, Geng, X, Darboux and Bäcklund transformations of the bidirectional Sawada--Kotera equation. Applied Mathematics and Computation. 2012, 218, 6963-6967.
  4. Zerarka, A, Ouamane, S, Attaf, S, On the functional variable method for finding exact solutions to a class of wave equations, Applied Mathematics and Computation. 2010, 217, 2897. Wang, M.L, Zhou, Y.B, Li, Z.B, Application of a homogeneous balance method to exact solutions of nonlinear equation in mathematical physics. Physics Letters. A. 1996, 216, 67-75.
  5. Bekir, A, Applications of the extended tanh method for coupled nonlinear evolution equations. Communications in Nonlinear Science and Numerical Simulation. 2008, 13, 1748-1757.
  6. Bekir, A, Application of the (G'⁄G)-expansion method for nonlinear evolution equations. Physics Letters A. 2008, 372, 3400-3406.
  7. Olver, P.J, Application of Lie groups to Differential Equations. Springer-Verlag, New York. 1993.
  8. Tascan, F, Bekir A, Koparan, M, Travelling wave solutions of nonlinear evolution equations by using the first integral method, Communications in Nonlinear Science & Numerical Simulation. 2009, 14, 1810-1815.
  9. Moore, K.R, Coupled Boussinesq equations and nonlinear waves in layered waveguides. (Doctoral dissertation, © KR Moore), 2013.
  10. Khusnutdinova, K.R, Coupled Klein-Gordon equations and energy exchange in two-component systems. The European Physical Journal Special Topics. 2007, 147(1), 45-72.
  11. Wazwaz, A.M, New travelling wave solutions to the Boussinesq and the Klein-Gordon equations, Communications in Nonlinear Science and Numerical Simulation. 2008, 13, 889-901.
  12. Chen, J, Yang, J, Yang, H, Single soliton solutions of the coupled nonlinear Klein-Gordon equations with power law nonlinearity. Applied Mathematics and Computation. 2014, 246, 184-191.
  13. Hirota, R, Ohta, Y, Hierarchies of coupled soliton equations. I, Journal of the Physical Society of Japan. 1991, 60, 798-809.
  14. Alagesan, T, Chung, Y, Nakkeeran, K, Soliton solutions of coupled nonlinear Klein-Gordon equations. Chaos, Solitons & Fractals. 2004, 21, 879-882.
  15. Alagesan, T, Chung, Y, Nakkeeran, K, Painlevé analysis of N-coupled nonlinear Klein-Gordon equations. J