Soliton solutions for perturbed Radhakrishnan-Kundu-Lakshmanan equation

Öz

To find some soliton solutions of the equation, the perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation has been considered. For this purpose, GKM (generalized Kudryashov method), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been applied to the perturbed RKL equation. First, considered the nonlinear partial differential equation, is reduced to an ordinary differential equation with the help of the traveling wave transformation. Afterward, obtained the algebraic equation system through the balance principle was solved with the help of Wolfram Mathematica 12. Thus, some new soliton solutions of the discussed equation have been obtained. Both 2D and 3D graphics have been drawn with the help of Wolfram Mathematica 12 by giving some values to obtained these new solutions.

Anahtar Kelimeler

• GKM
• perturbed RKL equation
• soliton solutions

Perturbe edilmiş Radhakrishnan-Kundu-Lakshmanan denklemi için soliton çözümler

Öz

Denklemin bazı soliton çözümlerini bulmak için perturbe edilmiş Radhakrishnan-Kundu-Lakshmanan (RKL) denklemi ele alınmıştır. Bu amaç için lineer olmayan evrim denklemleri (NLEEs)’nin çözüm yöntemlerinden biri olan GKM (genelleştirilmiş Kudryashov metodu), perturbe edilmiş RKL denklemine uygulanmıştır. İlk olarak ele alınan lineer olmayan kısmi diferansiyel denklem, hareketli dalga dönüşümü yardımıyla bir adi diferansiyel denkleme indirgenmiştir. Daha sonra denge prensibi ile elde edilen cebirsel denklem sistemi Wolfram Mathematica 12 yardımıyla çözülmüştür. Böylece ele alınmış olan denklemin bazı yeni soliton çözümleri elde edilmiştir. Elde edilen bu yeni çözümlere birtakım değerler verilerek Wolfram Mathematica 12 yardımıyla hem 2 boyutlu hem de 3 boyutlu grafiklerin çizimleri yapılmıştır

Anahtar Kelimeler

• GKM
• perturbe edilmiş RKL denklemi
• soliton çözümler

Kaynakça

1. Akbulut, A. and Taşcan, F., Application of conservation theorem and modified extended tanh-function method to (1+1)-dimensional nonlinear coupled Klein–Gordon–Zakharov equation, Chaos, Solitons & Fractals, 104, 33-40, (2017).
2. Ali, A., Seadawy, A.R. and Lu, D., Soliton solutions of the nonlinear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysis, Optik-International Journal for Light and Electron Optics, 145, 79-88, (2017).
3. Bulut, H., Akkilic, A.N. and Khalid, B.J., Soliton Solutions Of Hirota Equation and Hirota-Maccari System by the -Expansion Method, Advanced Mathematical Models & Applications, 6, 1, 22-30, (2021).
4. Ege, Ş.M., Traveling Wave Solutions For Two Physical Models via Extended Modified Kudryashov Method, Journal of the Institute of Science and Technology, 11, 1, 625-634, (2021).
5. Ekici, M., Optical solitons in birefringent fibers for Lakshmanan–Porsezian–Daniel model by extended Jacobi's elliptic function expansion scheme, Optik-International Journal for Light and Electron Optics, 172, 651-656, (2018).
6. Kocak, H. and Pinar, Z., On solutions of the fifth-order dispersive equations with porous medium type non-linearity, Waves in Random and Complex Media, 28, 3, 516-522, (2018).
7. Soliman, A.A., The Modified Extended Direct Algebraic Method for Solving Nonlinear Partial Differential Equations, International Journal of Nonlinear Science, 6, 2, 136-144, (2008).
8. Xu, T., Li, H., Zhang, H., Li, M. and Lan, S., Darboux transformation and analytic solutions of the discrete -symmetric nonlocal nonlinear Schrödinger equation, Applied Mathematics Letters, 63, 88-94, (2017).

9. Yel, G., Baskonus, H.M. and Bulut, H., Novel archetypes of new coupled Konno–Oono equation by using sine–Gordon expansion method, Optical and Quantum Electronics, 49, 9, 1-10, (2017).
10. Yıldırım, Y., Optical solitons with Biswas-Arshed equation by F-expansion method, Optik-International Journal for Light and Electron Optics, 227, 1-7, (2021).
11. Yokus, A. and Yavuz, M., Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation, Discrete & Continuous Dynamical Systems-S, 14, 7, 2591-2606, (2021).
12. Duran, S., Yokus, A., Durur, H. and Kaya, D., Refraction simulation of internal solitary waves for the fractional Benjamin-Ono equation in fluid dynamics, Modern Physics Letters B, 35, 26, 2150363, (2021).
13. Durur, H. And Yokuş, A., Discussions on diffraction and the dispersion for traveling wave solutions of the (2+1)-dimensional paraxial wave equation, Mathematical Sciences (2021).
14. Biswas, A., Optical soliton perturbation with Radhakrishnan-Kundu-Lakshmanan equation by traveling wave hypothesis, Optik-International Journal for Light and Electron Optics, 171, 217-220, (2018).
15. Biswas, A., Yildirim, Y., Yasar, E., Mahmood, M.F., Alshomrani, A.S., Zhou, Qin., Moshokoa, S.P. and Belic, M., Optical soliton perturbation for Radhakrishnan-Kundu-Lakshmanan equation with a couple of integration schemes, Optik-International Journal for Light and Electron Optics, 163, 126-136, (2018).
16. Ghanbari, B. and Gomez-Aguilar, J.F., Optical soliton solutions for the nonlinear Radhakrishnan-Kundu-Lakshmanan equation, Modern Physics Letters B, 33, 32, 1-15, (2019).
17. Barman, H.K., Islam, M.E. and Akbar, M.A., A study on the compatibility of the generalized Kudryashov method to determine wave solutions, Propulsion and Power Research, 10, 1, 95-105 (2021).
18. Gurefe, Y., The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative, Revista Mexicana de Fisica, 66, 6, 771-781, (2020).
19. Tuluce Demiray, S., New Soliton Solutions of Optical Pulse Envelope with Beta Time Derivative, Optik-International Journal for Light and Electron Optics, 223, 1-6, (2020).
20. Tuluce Demiray, S. and Bayrakci, U., Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM, Journal of the Institute of Science and Technology, 11, 2, 1481-1488, (2021).