KMM Sistemi ve Genelleştirilmiş Hiperelastik-Rod Dalga Denklemi için Soliton Çözümler

Bu çalışmada Kraenkel-Manna-Merle (KMM) sistemi ve genelleştirilmiş hiperelastik-rod dalga denklemi incelenmiştir. Bunun için lineer olmayan evrim denklemlerinin çözüm yöntemlerinden biri olan genelleştirilmiş Kudryashov metodu (GKM), KMM sistemine ve genelleştirilmiş hiperelastik-rod dalga denklemlerine uygulanmıştır. Ele alınan denklemler için bazı çözümler bulunmuş ve Wolfram Mathematica 12 kullanılarak iki ve üç boyutlu olarak görselleştirilmiştir.

Anahtar Kelimeler:

GKM, Kraenkel-Manna-Merle sistemi, Genelleştirilmiş hiperelastik-rod dalga denklemi, Soliton çözümleri

Solutions for KMM System and Generalized Hyperelastic-Rod Wave Equation

In this study, the Kraenkel-Manna-Merle (KMM) system and generalized hyperelastic-rod wave equation have been investigated. For this, generalized Kudryashov method (GKM), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been implemented to KMM system and generalized hyperelastic-rod wave equation. Some solutions to the discussed equations have been found and visualized using Wolfram Mathematica 12 in two and three dimensions.

Keywords:

GKM, Kraenkel-Manna-Merle system, Generalized hyperelastic-rod wave equation, Soliton Solutions,

PDF

___

Ananna SN., An, T., Asaduzzaman M., Miah MM. Solitary wave structures of a family of 3D fractional WBBM equation via the tanh–coth approach. Partial Differential Equations in Applied Mathematics 2022; 5: 1-6.
Akcagil S., Aydemir T., Gozukizil OF. Exact travelling wave solutions of nonlinear pseudoparabolic equations by using the G′/G Expansion Method. New Trends in Mathematical Sciences 2016; 4(4): 51-66.
Barman HK., Islam ME., Akbar MA. A study on the compatibility of the generalized Kudryashov method to determine wave solutions. Propulsion and Power Research 2021; 10(1): 95-105.
Bendahmane M., Coclite GM., Karlsen KH. H1-perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation. Mediterranean Journal of Mathematics 2006; 3(3): 419-432.
Biswas A., Yıldırım Y., Yaşar E., Alqahtani RT. Optical solitons for Lakshmanan–Porsezian–Daniel model with dual-dispersion by trial equation method. Optik 2018; 168: 432-439.
Coclite GM., Holden H., Karlsen KH. Global weak solutions to a generalized hyperelastic-rod wave equation. SIAM Journal on Mathematical Analysis 2005; 37(4): 1044-1069.
Duarte LGS., da Mota LACP. An efficient method for computing Liouvillian first integrals of planar polynomial vector fields. Journal of Differential Equations 2021; 300: 356-385.
Eslami M., Mirzazadeh M. Exact solutions of modified Zakharov–Kuznetsov equation by the homogeneous balance method. Ain Shams Engineering Journal 2014; 5(1): 221-225.
Gözükızıl ÖF., Akçağıl Ş. The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions. Advances in Difference Equations 2013; (1): 1-18.
Gurefe Y. The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative. Revista Mexicana de Física 2020; 66(6): 771-781.
Günay B., Kuo CK., Ma WX. An application of the exponential rational function method to exact solutions to the Drinfeld–Sokolov system. Results in Physics, 2021; 29: 1-8.
Holden H., Raynaud X. Global conservative solutions of the generalized hyperelastic-rod wave equation. Journal of Differential Equations 2007; 233(2): 448-484.
Jin XW., Lin J. Rogue wave, interaction solutions to the KMM system. Journal of Magnetism and Magnetic Materials 2020; 502: 1-9.
Kara S., Ünsal Ö. Analytical solutions to new forms of two nonlinear partial differential equations via two variable expansion method. Partial Differential Equations in Applied Mathematics 2022; 5: 1-7.
Kraenkel RA., Manna MA., Merle V. Nonlinear short-wave propagation in ferrites. Physical Review E, 2000; 61(1): 976-979. Kuetche VK., Nguepjouo FT., Kofane T. C. Engineering magnetic polariton system with distributed coefficients: Applications to soliton management. Chaos, Solitons Fractals 2014; 66: 17-30.
Li BQ., Ma YL. Rich soliton structures for the Kraenkel-Manna-Merle (KMM) system in ferromagnetic materials. Journal of Superconductivity and Novel Magnetism 2018; 31(6): 1773-1778.
Li BQ., Ma YL. Loop-like periodic waves and solitons to the Kraenkel–Manna–Merle system in ferrites. Journal of Electromagnetic Waves and Applications 2018; 32(10): 1275-1286.
Nguepjouo FT., Kuetche VK., Kofane TC. Soliton interactions between multivalued localized waveguide channels within ferrites. Physical Review E 2014; 89(6): 1-14.
Si HL., Li BQ. Two types of soliton twining behaviors for the Kraenkel–Manna–Merle system in saturated ferromagnetic materials. Optik 2018; 166: 49-55.
Tchokouansi HT., Kuetche VK., Kofane TC. On the propagation of solitons in ferrites: The inverse scattering approach. Chaos, Solitons Fractals 2016; 86: 64-74.
Tuluce Demiray S., Bayrakci U. Construction of Soliton Solutions for Chaffee-Infante Equation. Afyon Kocatepe University Journal of Science and Engineering 2021a; 21(5): 1046-1051.
Tuluce Demiray S., Bayrakci U. Soliton solutions of generalized third-order nonlinear Schrödinger equation by using GKM. Journal of the Institute of Science and Technology 2021b; 11(2): 1481-1488.
Tuluce Demiray S., Bayrakci U. Soliton solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp (-Ω (η))-expansion function method. Revista Mexicana de Física 2021c; 67(3): 393-402.
Younas U., Sulaiman TA., Yusuf A., Bilal M., Younis M., Rehman SU. New solitons and other solutions in saturated ferromagnetic materials modeled by Kraenkel–Manna–Merle system. Indian Journal of Physics 2022; 96(1): 181-191.