Travelling Wave Solutions for the Long–Short–Wave Interaction System Using the Unified Method

Uzun-Kısa-Dalga etkileşimi sistemi, düşük frekanslı uzun dalgalar ve yüksek frekanslı kısa dalgalar arasında önemli bir rol oynar. Önemli bir kompleks model olmasının yanı sıra, yerçekimi ve su dalgaları, plazma ve biyofizik, doğrusal olmayan optik gibi çeşitli fiziksel olgularla da ilgilidir. Bu sistem birçok araştırmacı tarafından ele alınmış ve farklı yöntemler kullanılarak bir çok çözümü elde edilmiştir. Bu çalışmada, uzun-kısa-dalga etkileşim sisteminin yeni solitary tip çözümleri, unified yöntem olarak elde edilecektir. Elde edilen çözümler önceki çözümlerin geliştirilmiş versiyonu olarak düşünülebilir. Bu çalışma aynı zamanda unified yöntemin etkinliğini de göstermektedir.

Anahtar Kelimeler:

Solitary tip çözüm, Uzun-Kısa-Dalga etkileşimi sistemi, Unified yöntem

Solitary Type Solutions for the Long–Short–Wave Interaction System Using the Unified Method

The Long-Short-Wave interaction system plays a significant role between low frequency long waves and high frequency short waves. Besides being an important complex model it is also related with several physical phenomenon such as, gravity and water waves, plasma and bio-physics, nonlinear optic. This system was handled by many researchers and solutions of this system were obtained by using different methods. In this paper, new solitary type solutions for the Long-short-wave interaction system are formaly drived by using different method namely the unified method. The obtained solutions can be considered as improved version of the previous solutions. This study also shows the efficiency of the unified method.

Keywords:

Solitary type solution, Long-short-wave interaction system, The unified method,

PDF

___

Wang, M. L., Wang, Y. M., Zhang, J. L. 2003. The periodic wave solutions for two systems of nonlinear wave equations. Chin. Phys., 12: 1341.
Bekir, A., Ünsal, Ö. 2012. Periodic and solitary wave solutions of coupled nonlinear wave equations using the first integral method, Phys. Scr. , 85: 065003.
Sirendaoerji. 2017. Constructing infinite number of exact travelling wave solutions of nonlinear evolution equations via an extended tanh-function method, International Journal of Nonlinear Science, 24: 161–168.
Huibin, L., Kelin, W. 1990. Exact solutions for some coupled nonlinear equations II, Journal of Physics A: Mathematical and General, 23: 4197-4105.
Malfliet, W., Hereman, W. 1996. The tanh method. I: Exact solutions of nonlinear evolution and wave equations, Phys. Scr., 54: 563-568.
Fan, E.G. 2000. Extended tanh-function method and its applications to nonlinear equations, Phys Lett. A, 277: 212-218.
El-Wakil, S. A. , El-Labany, S. K. , Zahran, M. A., Sabry, R. 2005. Modified extended tanh-function method and its applications to nonlinear equations, Appl. Math. Comput., 161: 403-412.
Khuri, S. A. 2004. A complex tanh-function method applied to nonlinear equations of Schrödinger type, Chaos, Solitons and Fractals, 20: 1037-1040.
Wang, M., Li, X., Zhang, J. 2008. The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A, 372: 417-423.
Gözükızıl, Ö. F., Akçağıl, Ş., Aydemir, T. 2016. Unification of all hyperbolic tangent function methods, Open Phys.,