(2+1)-boyutlu kompleks lineer olmayan üç bağlı Maccari modelinin modifiye edilmiş yeni Kudryashov yöntemi ile topolojik olmayan soliton çözümü

Yıl 2022, Sayı: 38, 173 - 178, 31.08.2022

Müslüm Özışık Ramazan Tekercioğlu

https://doi.org/10.31590/ejosat.1108958

Öz

Bu makale, yakın zamanda sunulan modifiye edilmiş yeni Kudryashov yöntemini (mNKM) kullanarak (2+1)-boyutlu kompleks lineer olmayan üç bağlı Maccari modelini (3-CCME) ele almaktadır. Bu makalenin amacı, araştırılan probleme daha önce uygulanmamış olan mKNM yöntemini uygulayarak 3-CCME probleminin topolojik olmayan soliton çözümünü elde etmektir. Önerilen yöntem başarılı bir şekilde uygulanarak, incelenen problemin topolojik olmayan soliton çözümünün yanı sıra, breather benzeri türünde soliton çözümü de elde edilmiş ve elde edilen sonuçlar 3D, 2D ve kontur grafik sunumları ile gösterilmiştir.

Anahtar Kelimeler

Kompleks lineer olmayan üç bağlı Maccari modeli;, Modifile edilmiş yeni Kudryashov yöntemi;, Soliton çözümü.

Non-topological soliton solution of (2+1)-dimensional complex three coupled nonlinear Maccari’s model via modified new Kudryashov scheme

Öz

This paper, deals with the (2+1)-dimensional complex three coupled nonlinear Maccari’s model (3-CCME) by utilizing recently presented modified new Kudryashov method (mNKM). The focus of this article is to obtain non-topological soliton solution of 3-CCME by applying mKNM method, which has not been applied before to the investigated problem. Applying the proposed method successfully, besides the non-topological soliton solution of the investigated problem, the breather-like type soliton solution was also obtained and the obtained results are depicted by the 3D, 2D and contour graphical presentations.

Anahtar Kelimeler

Complex three coupled nonlinear Maccari’s model;, Modified new Kudryashov scheme;, Soliton solution.

Kaynakça

• Fan, Engui, Hon, Y. (2002). Generalized tanh Method Extended to Special Types of Nonlinear Equations. Zeitschrift für Naturforschung A. 57. 10.1515/zna-2002-0809.
• Arnous, Ahmed. (2013). The modified simple equation method and its applications to (2+1)-dimensional systems of nonlinear evolution equations. Scientific research and essays. 8. 1973.
• Na, Sirendaoreji, Jiong, Sun. (2006). Auxiliary equation method for solving nonlinear partial differential equations. Physics Letters A. 309. 387-396. 10.1016/S0375-9601(03)00196-8.
• Chen, Yong, Wangc, Qi. (2005). A New Riccati Equation Rational Expansion Method and Its Application. Zeitschrift für Naturforschung A. 60. 1-6. 10.1515/zna-2005-1-201.
• Na, Sirendaoreji. (2018). Variable separated ODE method–A powerful tool for testing traveling wave solutions of nonlinear equations. 10.13140/RG.2.2.13369.01120.
• Muslum Ozisik. On the optical soliton solution of the (1+1)- dimensional perturbed NLSE in optical nano-fibers. Optik, 250:168233, Jan 2022.
• M. Ali Akbar, Lanre Akinyemi, Shao-Wen Yao, Adil Jhangeer, Hadi Rezazadeh, Mostafa M.A. Khater, Hijaz Ahmad, Mustafa Inc. (2021). Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method, Results in Physics, Volume 25, 104228
• Yakup Yıldırım, Nisa Çelik, Emrullah Yaşar. (2017). Nonlinear Schrödinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions, Results in Physics, Volume 7, Pages 3116-3123.
• Ghanbari, Behzad & Baleanu, Dumitru. (2019). New Solutions of Gardner's Equation Using Two Analytical Methods. Frontiers in Physics. 7. 10.3389/fphy.2019.00202.
• Cattani, C., Sulaiman, T.A., Baskonus, H.M. et al. (2018). Solitons in an inhomogeneous Murnaghan’s rod. Eur. Phys. J. Plus 133, 228.
• Mecelti, Amel, Triki, Houria, Azzouzi, Faiçal, Wei, Xiong, Biswas, Anjan, Yıldırım, Yakup, Alshehri, Hashim, Zhou, Qin. (2022). New chirped gray and kink self–similar waves in presence of quintic nonlinearity and self–steepening effect. Physics Letters A. 437. 128104. 10.1016/j.physleta.2022.128104.
• Biswas, Anjan, Berkemeyer, Trevor, Khan, Salam, Moraru, Luminita, Yıldırım, Yakup, Alshehri, Hashim. (2022). Highly Dispersive Optical Soliton Perturbation, with Maximum Intensity, for the Complex Ginzburg–Landau Equation by Semi-Inverse Variation. Mathematics. 10. 987. 10.3390/math10060987.
• Gonzalez-Gaxiola, Oswaldo, Biswas, Anjan, Yildirim, Yakup, Alshehri, Hashim. (2022). Highly dispersive optical solitons in birefringent fibers having Kerr law of refractive index by Laplace–Adomian decomposition. Optik. 257. 168788. 10.1016/j.ijleo.2022.168788.
• Arnous, Ahmed, Biswas, Anjan, Kara, Abdul, Milovic, Daniela, Yıldırım, Yakup, Alshehri, Hashim. (2022). Sequel to cubic‐quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov's method. IET Optoelectronics. 10.1049/ote2.12065.
• Triki, Houria, Zhou, Qin, Liu, Wenjun, Biswas, Anjan, Moraru, Luminita, Yıldırım, Yakup, Alshehri, Hashim, Belic, Milivoj. (2022). Chirped optical soliton propagation in birefringent fibers modeled by coupled Fokas-Lenells system. Chaos, Solitons & Fractals. 155. 111751. 10.1016/j.chaos.2021.111751.
• Muniyappan, Annamalai, Amirthani, Shanmugham, Chandrika, Palanivel, Biswas, Anjan, Yıldırım, Yakup, Alshehri, Hashim, Maturi, Dalal, Al-Bogami, Dalal. (2022). Dark solitons with anti–cubic and generalized anti–cubic nonlinearities in an optical fiber. Optik. 255. 168641. 10.1016/j.ijleo.2022.168641.
• Kudryashov, Nikolay, Biswas, Anjan. (2022). Optical solitons of nonlinear Schrödi̇nger’s equation with arbitrary dual–power law parameters. Optik. 252. 168497. 10.1016/j.ijleo.2021.168497.
• Zahran, Emad, Rezazadeh, Hadi, Shehata, Maha. (2019). New Solitary Wave Solutions to the Three Coupled Nonlinear Maccari's-System with a Complex Structure. 399.
• Ahmad Neirameh. (2016). New analytical solutions for the coupled nonlinear Maccari’s system, Alexandria Engineering Journal, Volume 55, Issue 3, Pages 2839-2847.
• Mustafa Inc, Aliyu Isa Aliyu, Abdullahi Yusuf, Dumitru Baleanu and Elif Nuray. (2018). Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes. Modern Physics Letters BVol. 32, No. 02, 1850014.
• Vahidi, Javad, Zekavatmand, Sayyed, Rezazadeh, Hadi, Inc, Mustafa, Akinlar, Mehmet, Chu, Yuming. (2021). New solitary wave solutions to the coupled Maccari’s system. Results in Physics. 21. 103801. 10.1016/j.rinp.2020.103801.
• Zahran, Emad, Shehata, Maha, Mirhosseini-Alizamini, Seyed Mehdi, Alam, Md. Nur, Akinyemi, Lanre. (2021). Exact propagation of the isolated waves model described by the three coupled nonlinear Maccari’s system with complex structure. International Journal of Modern Physics B. 10.1142/S0217979221501939.
• Hanan A. Alkhidhr, Mahmoud A.E. Abdelrahman. (2022). Wave structures to the three coupled nonlinear Maccari’s systems in plasma physics, Results in Physics, Volume 33, 105092.
• Elsayed M.E. Zayed, Mohamed E.M. Alngar, Anjan Biswas, Mir Asma, Mehmet Ekici, Abdullah K. Alzahrani, Milivoj R. Belic. (2020). Optical solitons and conservation laws with generalized Kudryashov’s law of refractive index, Chaos, Solitons & Fractals, Volume 139, 110284.
• Saha, A., Ali, K.K., Rezazadeh, H. et al. (2021). Analytical optical pulses and bifurcation analysis for the traveling optical pulses of the hyperbolic nonlinear Schrödinger equation. Opt Quant Electron 53, 150.
• Khalid K. Ali, M.S. Mehanna. (2021). Traveling wave solutions and numerical solutions of Gilson–Pickering equation, Results in Physics, Volume 28, 104596.