Genişletilerek Düzenlenmiş Kudryashov Yöntemi ile İki Fiziksel Modelinin Hareketli Dalga Çözümleri

Abstract

Bu makalede, matematiksel fizikte yer alan Schrödinger denkleminin özel durumları olan Biswas-Milovic denklemi ve Gerdjikov-Ivanov denklemini çözmek için genişletilerek düzenlenmiş Kudryashov yöntemini (EMKM) öneriyoruz. Bu denklemler için parametrelerin özel değerleri alındığında rasyonel fonksiyon, üstel fonksiyon ve hiperbolik fonksiyon formları ile gösterilen birçok yeni genişletilmiş dalga çözümü elde edildi. Sonuçlar, EMKM'nin doğrusal olmayan kısmi diferansiyel denklemleri çözmek için etkili bir yöntem olduğunu göstermektedir.

Keywords

• Biswas-Milovic denklemi
• Gerdjikov-Ivanov denklemi
• genişletilerek düzenlenmiş Kudryashov yöntemi

Traveling Wave Solutions For Two Physical Models via Extended Modified Kudryashov Method

Abstract

In this paper, we propose the extended modified Kudryashov method (EMKM) for solving the Biswas-Milovic equation and Gerdjikov-Ivanov equation which are commonly special cases of Schrödinger equation in mathematical physics. We received many new extended traveling wave solutions when the special values of the parameters are taken for these equations which are pointed out by rational function, exponential function and hyperbolic function forms. The results show that EMKM is advantageous mathematical technique for solving nonlinear partial differential equations.

Keywords

• Biswas-Milovic equation
• Gerdjikov-Ivanov equation
• extended modified Kudryashov method

References

1. Arshed S, 2018. Two reliable techniques for the soliton solutions of perturbed Gerdjikov-Ivanov equation. Optik, 164: 93-99.
2. Biswas A, Ekici M, Sonmezoglu A, Triki H, Alshomrani AS, Zhour Q, Moshokoa SP, Belic M, 2018. Optical soltions for Gerdjjikov-Ivanov model by extended trial equation scheme. Optik,134: 1241-1248.
3. Biswas A, Ekici M, Sonmezoglu A, Triki H, Zhour Q, Moshokoa SP, Belic M, 2018. Dispersive optical solitons with differential group delay by extended trial equation method, Optik, 158: 790-798.
4. Ege SM, Misirli E, 2012. The modified Kudryashov method for solving some evolution equations. AIP Conference. Proceedings, 1470: 244-246.
5. Eslami M, Neirameh A, 2018. New analytic solutions for higher order nonlinear Schrödinger equation in optical fibers. Optical and Quantum Electronics, 50 (47): 1-8.
6. Hosseini K, Samadi F, Kumar D, Faridi M, 2018. New optical solitons of cubic-quartic nonlinear Schrödinger equation. Optik, 157: 1101-1105.
7. Hosseini K, Zabihi A, Samadani F, Ansari R, 2018. New explicit analytic solutions of the unstable nonlinear Schrödinger's equation using the exp and hyperbolic function methods. Optical and Quantum Electronics, 50 (19): 1-8.
8. Kadkhda N, Jafari H, 2017. Analytical solutions of the Gerdjikov–Ivanov equation by using〖exp(〗⁡〖φ(ξ))〗-expansion method. Optik, 139: 72-76.

9. Mirzazadeh M, Eslami M, Arnous AH, 2015. Dark optical solitons of Biswas-Milovic equation with dual-power law nonlinearity. The European Physical Journal Plus, 130 (4): 1-7.
10. Mirzazadeh M, Ekici M, Zhou Q, Sonmezoglu A, 2017. Analytical study of solitons in the fiber wave guide with power law nonlinearity, 101: 493-506.
11. Najafi M, Arbabi S, 2016. Dark soliton and periodic wave solutions of the Biswas-Milovic equation. Optik, 127: 2679-2619.
12. Raza N, Abdullah M, Butt AR, 2018. Analytical soliton solutions of Biswas–Milovic equation in Kerr and non-Kerr law media. Optik, 157: 993-1002.
13. Sayed EL, Zayed ME, Al-Nowehy AG, 2016. Analytic solutions of the Biswas-Milovic equation the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method. Open Physics, 14: 129-139.
14. Taghizadeh N, Mirzazadeh M, Farahrooz F, 2011. Analytic solutions of the nonlinear Schrödinger equation by the first integral method. Journal of Mathematical Analysis and Applications, 374: 549-553.
15. Triki H, Biswas A, 2011. Dark solitons for a generalized nonlinear Schrödinger equation with parabolic law and dual-power law nonlinearities, Mathematical Methods in the Applied Sciences, 34: 958-962.
16. Triki H, Alqahtani RT, Zhou Q, Biswas A, 2017. New envelope solitions for Gerdjikov-Ivanov model in nonlinear fiber optics. SuperlatticesandMicrostructures, 111: 326-334.
17. Zayed EME, Al-Nowehy AG, 2017. Analytic solutions and optical soliton solutions of the nonlinear Biswas–Milovic equation with dual-power law nonlinearity. Acta Physıca Polonıca A, 131(2): 240-251.
18. Zhou Z, Ekici M, Sonmezoglu A, Mirzazadeh M, Eslami M, 2016. Analytical study of solitons to Biswas–Milovic model in nonlinear optics. Journal of Modern Optics, 63(21): 2131-2137.