Research Article
Year 2022,
Volume: 8 Issue: 2, 54 - 59, 30.12.2022
Abstract
In this study, Kraenkel-Manna-Merle (KMM) system is discussed. Sine-Gordon expansion method (SGEM), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been applied to this system. Thus, by applying this method for the first time, some dark soliton, bright soliton, and dark-bright soliton solutions of the KMM system have been obtained. In addition, by giving specific values to the achieved solutions, 2D and 3D graphics of the solutions were plotted by way of the Wolfram Mathematica 12 program.
Keywords
References
- Kumar S. and Rani S., “Lie symmetry reductions and dynamics of soliton solutions of (2+1)-dimensional Pavlov equation”, Pramana Journal Physics, 94, 116, 2020.
- Bilal M., Younas U. and Ren J., “Dynamics of exact soliton solutions in the double-chain model of deoxyribonucleic acid”, Mathematical Methods in the Applied Sciences, 44(17), 13357-13375, 2021.
- Dutta H., Günerhan H., Ali K.K. and Yilmazer R., “Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative”, Frontiers in Physics, 8, 62, 2020.
- Gepreel K.A., “Exact Soliton Solutions for Nonlinear Perturbed Schrödinger Equations with Nonlinear Optical Media”, Applied Sciences, 10(24), 8929, 2020.
- Zafar A., Ali K.K., Raheel M., Jafar N. and Nisar K.S., “Soliton solutions to the DNA Peyrard–Bishop equation with beta-derivative via three distinctive approaches”, The European Physical Journal Plus, 135, 726, 2020.
- Mathanaranjan T., “Soliton Solutions of Deformed Nonlinear Schrödinger Equations Using Ansatz Method”, International Journal of Applied and Computational Mathematics, 7, 159, 2021.
- Souleymanou A., Korkmaz A., Rezazadeh H., Mukam S.P.T. and Bekir A., “Soliton solutions in different classes for the Kaup–Newell model equation”, Modern Physics Letters B, 34(03), 2050038, 2020.
- Almatrafi M.B., Alharbi A.R. and Tunç C., “Constructions of the soliton solutions to the good Boussinesq equation”, Advances in Difference Equations, 2020(629), 1-14, 2020.
- Durur H., “Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G’/G)-expansion method”, Modern Physics Letters B, 34(03), 2050036, 2020.
- Durur H., Kurt A., Tasbozan O., “New travelling wave solutions for KdV6 equation using sub equation method”, Applied Mathematics and Nonlinear Sciences, 5(1), 455-460, 2020.
- Durur H., Yokus A., “Exact solutions of (2+ 1)-Ablowitz-Kaup-Newell-Segur equation”, Applied Mathematics and Nonlinear Sciences, 6(2), 381-386, 2020.
- Tanaka M., Ohya S. and Hai P.N., “Recent progress in III-V based ferromagnetic semiconductors: band structure, Fermi level, and tunneling transport”, Applied Physics Reviews, 1(1), 1-26, 2014.
- Liu W., Pang L., Han H., Liu M., Lei M., Fang S., Teng H. and Wei Z., “Tungsten disulfide saturable absorbers for 67 fs mode-locked erbium-doped fiber lasers”, Optics Express, 25(3), 2950–2959, 2017.
- Ciornei M.C., Rubi J.M. and Wegrowe J.E., “Magnetization dynamics in the inertial regime: Nutation predicted at short time scales”, Physical Review B, 83(2), 020410, 2011.
- Dani I., Tahiri N., Ez-Zahraouy H. and Benyoussef A., “Ferromagnetic and antiferromagnetic properties in nano-films with RKKY interaction”, Superlattices Microstructures, 85, 894–900, 2015.
- Hajati Y. and Rashidian Z., “Gate-controlled spin and valley polarization transport in a ferromagnetic/nonmagnetic/ferromagnetic silicene junction”, Superlattices Microstructures, 92, 264–277, 2016.
- Kayani Z.N., Kausar T., Riaz S. and Naseem S., “Effect of aluminum doping concentration on optical, magnetic and microstructural properties of MnZnO thinfilms”, Optik, 144, 172–179, 2017.
- El-Desoky M.M., Ayoua M.S., Mostafa M.M. and Ahmed M.A., “Multiferroic properties of nanostructured barium doped bismuth ferrite”, Journal of Magnetism and Magnetic Materials, 404, 68-73, 2016.
- Mansour S.F., Abdo M.A. and Kzar F.L., “Effect of Cr dopant on the structural, magnetic and dielectric properties of Cu-Zn nanoferrites”, Journal of Magnetism and Magnetic Materials, 465 (1), 176-185, 2018.
- Tuluce Demiray S., Pandir Y. and Bulut H., “New solitary wave solutions of Maccari system”, Ocean Engineering, 103, 153–159, 2015.
- Kraenkel R.A., Manna M.A. and Merle V., “Nonlinear short-wave propagation in ferrites”, Physical Review E, 61(1), 976–979, 2000.
- Nguepjouo F.T., Kuetche V.K. and Kofane T.C., “Soliton interactions between multivalued localized waveguide channels within ferrites”, Physical Review E, 89, 063201, 2014.
- Younas U., Sulaiman T.A., Yusuf A., Bilal M., Younis M. and Rehman S.U., “New solitons and other solutions in saturated ferromagnetic materials modeled by Kraenkel–Manna–Merle system”, Indian Journal of Physics, 96, 181-191, 2022.
- Li B.Q. and Ma Y.L., “Rich Soliton Structures for the Kraenkel-Manna-Merle (KMM) System in Ferromagnetic Materials”, Journal of Superconductivity and Novel Magnetism, 31, 1773-1778, 2018.
- Li B.Q. and Ma Y.L., “Oscillation rogue waves for the Kraenkel–Manna–Merle system in ferrites”, Journal of Magnetism and Magnetic Materials, 537, 168182, 2021.
- Raza N., Hassan Z., Butt A., Rahman R. and Abdel-Aty A.H., “New and more dual-mode solitary wave solutions for the Kraenkel-Manna-Merle system incorporating fractal effects”, Authorea Preprints; 1-24, 2021.
- Ur-Rehman S., Bilal M. and Ahmad J., “Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method”, Journal of Magnetism and Magnetic Materials, 538, 168245, 2021.
- Si H.L. and Li B.Q., “Two types of soliton twining behaviors for the Kraenkel–Manna–Merle system in saturated ferromagnetic materials”, Optik, 166, 49-55, 2018.
- Ali K.K., Osman M.S. and Abdel-Aty M., “New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method”, Alexandria Engineering Journal, 59(3), 1191-1196, 2020.
- Korkmaz A., Hepson O.E., Hosseini K., Rezazadeh H. and Eslami M., “Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class”, Journal of King Saud University-Science, 32(1), 567-574, 2020.
- Kumar D., Hosseini K. and Samadani F., “The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics”, Optik, Vol:149, 439-446, 2017.
- Kundu P.R., Fahim M.R.A., Islam M.E. and Akbar M.A., “The sine-Gordon expansion method for higher-dimensional NLEEs and parametric analysis”, Heliyon, 7(3), e06459, 1-8, 2021.
- Yan Z. and Zhang H., “New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics”, Physics Letters A, 252(6), 291-296, 1999.
Year 2022,
Volume: 8 Issue: 2, 54 - 59, 30.12.2022
Abstract
Bu çalışmada, Kraenkel-Manna-Merle sistemi ele alınmıştır. Doğrusal olmayan evrim denklemlerinin çözüm yöntemlerinden biri olan sinüs-Gordon açılım yöntemi bu sisteme uygulanmıştır. Böylece ilk kez bu yöntem uygulanarak KMM sisteminin bazı dark soliton, bright soliton ve dark-bright soliton çözümleri elde edilmiştir. Ayrıca elde edilen çözümlere belirli değerler verilerek Wolfram Mathematica 12 programı aracılığıyla çözümlerin 2 boyutlu ve 3 boyutlu grafikleri çizilmiştir.
Keywords
References
- Kumar S. and Rani S., “Lie symmetry reductions and dynamics of soliton solutions of (2+1)-dimensional Pavlov equation”, Pramana Journal Physics, 94, 116, 2020.
- Bilal M., Younas U. and Ren J., “Dynamics of exact soliton solutions in the double-chain model of deoxyribonucleic acid”, Mathematical Methods in the Applied Sciences, 44(17), 13357-13375, 2021.
- Dutta H., Günerhan H., Ali K.K. and Yilmazer R., “Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative”, Frontiers in Physics, 8, 62, 2020.
- Gepreel K.A., “Exact Soliton Solutions for Nonlinear Perturbed Schrödinger Equations with Nonlinear Optical Media”, Applied Sciences, 10(24), 8929, 2020.
- Zafar A., Ali K.K., Raheel M., Jafar N. and Nisar K.S., “Soliton solutions to the DNA Peyrard–Bishop equation with beta-derivative via three distinctive approaches”, The European Physical Journal Plus, 135, 726, 2020.
- Mathanaranjan T., “Soliton Solutions of Deformed Nonlinear Schrödinger Equations Using Ansatz Method”, International Journal of Applied and Computational Mathematics, 7, 159, 2021.
- Souleymanou A., Korkmaz A., Rezazadeh H., Mukam S.P.T. and Bekir A., “Soliton solutions in different classes for the Kaup–Newell model equation”, Modern Physics Letters B, 34(03), 2050038, 2020.
- Almatrafi M.B., Alharbi A.R. and Tunç C., “Constructions of the soliton solutions to the good Boussinesq equation”, Advances in Difference Equations, 2020(629), 1-14, 2020.
- Durur H., “Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G’/G)-expansion method”, Modern Physics Letters B, 34(03), 2050036, 2020.
- Durur H., Kurt A., Tasbozan O., “New travelling wave solutions for KdV6 equation using sub equation method”, Applied Mathematics and Nonlinear Sciences, 5(1), 455-460, 2020.
- Durur H., Yokus A., “Exact solutions of (2+ 1)-Ablowitz-Kaup-Newell-Segur equation”, Applied Mathematics and Nonlinear Sciences, 6(2), 381-386, 2020.
- Tanaka M., Ohya S. and Hai P.N., “Recent progress in III-V based ferromagnetic semiconductors: band structure, Fermi level, and tunneling transport”, Applied Physics Reviews, 1(1), 1-26, 2014.
- Liu W., Pang L., Han H., Liu M., Lei M., Fang S., Teng H. and Wei Z., “Tungsten disulfide saturable absorbers for 67 fs mode-locked erbium-doped fiber lasers”, Optics Express, 25(3), 2950–2959, 2017.
- Ciornei M.C., Rubi J.M. and Wegrowe J.E., “Magnetization dynamics in the inertial regime: Nutation predicted at short time scales”, Physical Review B, 83(2), 020410, 2011.
- Dani I., Tahiri N., Ez-Zahraouy H. and Benyoussef A., “Ferromagnetic and antiferromagnetic properties in nano-films with RKKY interaction”, Superlattices Microstructures, 85, 894–900, 2015.
- Hajati Y. and Rashidian Z., “Gate-controlled spin and valley polarization transport in a ferromagnetic/nonmagnetic/ferromagnetic silicene junction”, Superlattices Microstructures, 92, 264–277, 2016.
- Kayani Z.N., Kausar T., Riaz S. and Naseem S., “Effect of aluminum doping concentration on optical, magnetic and microstructural properties of MnZnO thinfilms”, Optik, 144, 172–179, 2017.
- El-Desoky M.M., Ayoua M.S., Mostafa M.M. and Ahmed M.A., “Multiferroic properties of nanostructured barium doped bismuth ferrite”, Journal of Magnetism and Magnetic Materials, 404, 68-73, 2016.
- Mansour S.F., Abdo M.A. and Kzar F.L., “Effect of Cr dopant on the structural, magnetic and dielectric properties of Cu-Zn nanoferrites”, Journal of Magnetism and Magnetic Materials, 465 (1), 176-185, 2018.
- Tuluce Demiray S., Pandir Y. and Bulut H., “New solitary wave solutions of Maccari system”, Ocean Engineering, 103, 153–159, 2015.
- Kraenkel R.A., Manna M.A. and Merle V., “Nonlinear short-wave propagation in ferrites”, Physical Review E, 61(1), 976–979, 2000.
- Nguepjouo F.T., Kuetche V.K. and Kofane T.C., “Soliton interactions between multivalued localized waveguide channels within ferrites”, Physical Review E, 89, 063201, 2014.
- Younas U., Sulaiman T.A., Yusuf A., Bilal M., Younis M. and Rehman S.U., “New solitons and other solutions in saturated ferromagnetic materials modeled by Kraenkel–Manna–Merle system”, Indian Journal of Physics, 96, 181-191, 2022.
- Li B.Q. and Ma Y.L., “Rich Soliton Structures for the Kraenkel-Manna-Merle (KMM) System in Ferromagnetic Materials”, Journal of Superconductivity and Novel Magnetism, 31, 1773-1778, 2018.
- Li B.Q. and Ma Y.L., “Oscillation rogue waves for the Kraenkel–Manna–Merle system in ferrites”, Journal of Magnetism and Magnetic Materials, 537, 168182, 2021.
- Raza N., Hassan Z., Butt A., Rahman R. and Abdel-Aty A.H., “New and more dual-mode solitary wave solutions for the Kraenkel-Manna-Merle system incorporating fractal effects”, Authorea Preprints; 1-24, 2021.
- Ur-Rehman S., Bilal M. and Ahmad J., “Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method”, Journal of Magnetism and Magnetic Materials, 538, 168245, 2021.
- Si H.L. and Li B.Q., “Two types of soliton twining behaviors for the Kraenkel–Manna–Merle system in saturated ferromagnetic materials”, Optik, 166, 49-55, 2018.
- Ali K.K., Osman M.S. and Abdel-Aty M., “New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method”, Alexandria Engineering Journal, 59(3), 1191-1196, 2020.
- Korkmaz A., Hepson O.E., Hosseini K., Rezazadeh H. and Eslami M., “Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class”, Journal of King Saud University-Science, 32(1), 567-574, 2020.
- Kumar D., Hosseini K. and Samadani F., “The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics”, Optik, Vol:149, 439-446, 2017.
- Kundu P.R., Fahim M.R.A., Islam M.E. and Akbar M.A., “The sine-Gordon expansion method for higher-dimensional NLEEs and parametric analysis”, Heliyon, 7(3), e06459, 1-8, 2021.
- Yan Z. and Zhang H., “New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics”, Physics Letters A, 252(6), 291-296, 1999.
There are 33 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Journals |
| Authors | |
| Early Pub Date | November 2, 2022 |
| Publication Date | December 30, 2022 |
| Published in Issue | Year 2022 Volume: 8 Issue: 2 |
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