Araştırma Makalesi
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New Soliton Solutions Arising in Some NLEEs

Yıl 2022, , 51 - 59, 27.06.2022
https://doi.org/10.17678/beuscitech.1115396

Öz

We have worked on (2+1)-dimensional dissipative long wave system (DLWS) and (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation. We have applied GKM, which has been obtained by generalizing the Kudryashov method, to the (2+1)- dimensional DLWS and (2+1)-dimensional DJKM equation. Thus, we have got some new soliton solutions of handled system and equation. We have plotted 2D and 3D surfaces of these acquired results by using Wolfram Mathematica 12. Then, we have shown the validity of the acquired solutions.

Kaynakça

  • Adem, A.R., Yıldırım, Y. and Yaşar, E. 2019. Complexiton solutions and soliton solutions: (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Pramana Journal Physics, 92 (36), 1-12.
  • Ali, K. K., Zahibi, A., Rezazadeh, H., Ansari, R., and Inc, M. 2021. Optical soliton with Kudryashov’s equation via sine-Gordon expansion and Kudryashov methods. Optical and Quantum Electronics, 53 (362), 1-15.
  • Chang, L., Liu, H. and Xin, X. 2020. Lie symmetry analysis, bifurcations and exact solutions for the (2+1)-dimensional dissipative long wave system. Journal of Applied Mathematics and Computing, 64, 807-823.
  • Cinar, M., Onder, I., Secer, A., Yusuf, A., Sulaiman, T. A., Bayram, M. and Aydin, H. 2021. Soliton Solutions of (2 + 1) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational sine-cosine and sinh-cosh Method. International Journal of Applied and Computational Mathematics, 7 (135), 1-17.
  • Dusunceli, F., Celik, E., Askin, M. and Bulut, H. 2021. New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method. Indian Journal of Physics, 95 (2), 309-314.
  • Gao, W., Ismael, H. F., Bulut, H. and Baskonus, H. M. 2020. Instability modulation for the (2+1)-dimension paraxial wave equation and its new optical soliton solutions in Kerr media. Physica Scripta, 95 (3), 1-17.
  • Ghanbari, B. and Inc, M. 2018. A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation. The European Physical Journal Plus, 133 (142), 1-18.
  • Guo, F. and Lin, J. 2019. Interaction solutions between lump and stripe soliton to the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Nonlinear Dynamics, 96, 1233-1241.
  • Ismael, H. F., Bulut, H., Park, C. and Osman, M. S. 2020. M-lump, N-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Results in Physics, 19, 103329.
  • Kaplan, M. and Akbulut, A. 2021. The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method. Optical and Quantum Electronics, 53 (498), 1-21.
  • Kumar, D. and Kaplan, M. 2018. Application of the modified Kudryashov method to the generalized Schrödinger–Boussinesq equations. Optical and Quantum Electronics, 50 (329), 1-14.
  • Manafian, J., Ivatloo, B. M. and Abapour M. 2020. Breather wave, periodic, andcross-kink solutions to the generalized Bogoyavlensky-Konopelchenko equation. Mathematical Methods in the Applied Sciences, 43 (4), 1753–1774.
  • Mirzazadeh, M., Akinyemi, L., Şenol, M. and Hosseini K. 2021. A variety of solitons to the sixth-order dispersive (3+1)-dimensional nonlinear time-fractional Schrödinger equation with cubic-quintic-septic nonlinearities. Optik-International Journal for Light and Electron Optics, 241, 166318.
  • Pandır, Y. and Eren, S. 2021. Exact Solutions of the Two Dimensional KdV-Burger Equation by Generalized Kudryashov Method. Journal of the Institute of Science and Technology, 11 (1), 617-624.
  • Pu, J. C. and Hu, H. C. 2019. Exact solitary wave solutions for two nonlinear systems. Indian Journal of Physics, 93 (2), 229-234.
  • Rani, A., Zulfiqar, A., Ahmad, J. and Hassan, Q. M. U. 2021. New soliton wave structures of fractional Gilson-Pickering equation using tanh-coth method and their applications. Result in Physics, 29, 104724.
  • Singh, M. and Gupta, R. K. 2018. On Painlevé analysis, symmetry group and conservation laws of Date-Jimbo-Kashiwara-Miwa equation. Int J Appl Comput Math, 4 (88), 1-15.
  • Tuluce Demiray, S. 2020. New solutions of Biswas-Arshed equation with beta time derivative. Optik-International Journal for Light and Electron Optics, 222, 165405.
  • Tuluce Demiray, S. and Bayrakci, U. 2021. Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp -expansion function method. Revista Mexicana de Fisica, 67 (3), 393-402.
  • Yang, J. and Feng, Q. 2021. The soliton solutions and evolution of the (2+1)-dimensional dissipative long wave equation. Results in Physics, 21, 103974.
  • Yaslan, H. Ç. and Girgin, A. 2019. Exp-function method for the conformable space-time fractional STO, ZKBBM and coupled Boussinesq equations. Arab Journal of Basic and Applied Sciences, 26 (1), 163-170.
  • Yokus, A., Durur, H., Ahmad, H. and Yao, S.W. 2020. Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation. Mathematics, 8 (6), 1-16.
  • Yuan, Y. Q., Tian, B., Sun, W. R., Chai, J. and Liu, L. 2017. Wronskian and Grammian solutions for a (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation. Computers and Mathematics with Applications, 74 (4), 873-879.
Yıl 2022, , 51 - 59, 27.06.2022
https://doi.org/10.17678/beuscitech.1115396

Öz

Kaynakça

  • Adem, A.R., Yıldırım, Y. and Yaşar, E. 2019. Complexiton solutions and soliton solutions: (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Pramana Journal Physics, 92 (36), 1-12.
  • Ali, K. K., Zahibi, A., Rezazadeh, H., Ansari, R., and Inc, M. 2021. Optical soliton with Kudryashov’s equation via sine-Gordon expansion and Kudryashov methods. Optical and Quantum Electronics, 53 (362), 1-15.
  • Chang, L., Liu, H. and Xin, X. 2020. Lie symmetry analysis, bifurcations and exact solutions for the (2+1)-dimensional dissipative long wave system. Journal of Applied Mathematics and Computing, 64, 807-823.
  • Cinar, M., Onder, I., Secer, A., Yusuf, A., Sulaiman, T. A., Bayram, M. and Aydin, H. 2021. Soliton Solutions of (2 + 1) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational sine-cosine and sinh-cosh Method. International Journal of Applied and Computational Mathematics, 7 (135), 1-17.
  • Dusunceli, F., Celik, E., Askin, M. and Bulut, H. 2021. New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method. Indian Journal of Physics, 95 (2), 309-314.
  • Gao, W., Ismael, H. F., Bulut, H. and Baskonus, H. M. 2020. Instability modulation for the (2+1)-dimension paraxial wave equation and its new optical soliton solutions in Kerr media. Physica Scripta, 95 (3), 1-17.
  • Ghanbari, B. and Inc, M. 2018. A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation. The European Physical Journal Plus, 133 (142), 1-18.
  • Guo, F. and Lin, J. 2019. Interaction solutions between lump and stripe soliton to the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Nonlinear Dynamics, 96, 1233-1241.
  • Ismael, H. F., Bulut, H., Park, C. and Osman, M. S. 2020. M-lump, N-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Results in Physics, 19, 103329.
  • Kaplan, M. and Akbulut, A. 2021. The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method. Optical and Quantum Electronics, 53 (498), 1-21.
  • Kumar, D. and Kaplan, M. 2018. Application of the modified Kudryashov method to the generalized Schrödinger–Boussinesq equations. Optical and Quantum Electronics, 50 (329), 1-14.
  • Manafian, J., Ivatloo, B. M. and Abapour M. 2020. Breather wave, periodic, andcross-kink solutions to the generalized Bogoyavlensky-Konopelchenko equation. Mathematical Methods in the Applied Sciences, 43 (4), 1753–1774.
  • Mirzazadeh, M., Akinyemi, L., Şenol, M. and Hosseini K. 2021. A variety of solitons to the sixth-order dispersive (3+1)-dimensional nonlinear time-fractional Schrödinger equation with cubic-quintic-septic nonlinearities. Optik-International Journal for Light and Electron Optics, 241, 166318.
  • Pandır, Y. and Eren, S. 2021. Exact Solutions of the Two Dimensional KdV-Burger Equation by Generalized Kudryashov Method. Journal of the Institute of Science and Technology, 11 (1), 617-624.
  • Pu, J. C. and Hu, H. C. 2019. Exact solitary wave solutions for two nonlinear systems. Indian Journal of Physics, 93 (2), 229-234.
  • Rani, A., Zulfiqar, A., Ahmad, J. and Hassan, Q. M. U. 2021. New soliton wave structures of fractional Gilson-Pickering equation using tanh-coth method and their applications. Result in Physics, 29, 104724.
  • Singh, M. and Gupta, R. K. 2018. On Painlevé analysis, symmetry group and conservation laws of Date-Jimbo-Kashiwara-Miwa equation. Int J Appl Comput Math, 4 (88), 1-15.
  • Tuluce Demiray, S. 2020. New solutions of Biswas-Arshed equation with beta time derivative. Optik-International Journal for Light and Electron Optics, 222, 165405.
  • Tuluce Demiray, S. and Bayrakci, U. 2021. Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp -expansion function method. Revista Mexicana de Fisica, 67 (3), 393-402.
  • Yang, J. and Feng, Q. 2021. The soliton solutions and evolution of the (2+1)-dimensional dissipative long wave equation. Results in Physics, 21, 103974.
  • Yaslan, H. Ç. and Girgin, A. 2019. Exp-function method for the conformable space-time fractional STO, ZKBBM and coupled Boussinesq equations. Arab Journal of Basic and Applied Sciences, 26 (1), 163-170.
  • Yokus, A., Durur, H., Ahmad, H. and Yao, S.W. 2020. Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation. Mathematics, 8 (6), 1-16.
  • Yuan, Y. Q., Tian, B., Sun, W. R., Chai, J. and Liu, L. 2017. Wronskian and Grammian solutions for a (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation. Computers and Mathematics with Applications, 74 (4), 873-879.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Uğur Bayrakcı 0000-0002-1765-2318

Şeyma Tülüce Demiray 0000-0002-8027-7290

Vehpi Yıldırım 0000-0003-3837-4756

Yayımlanma Tarihi 27 Haziran 2022
Gönderilme Tarihi 11 Mayıs 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

IEEE U. Bayrakcı, Ş. Tülüce Demiray, ve V. Yıldırım, “New Soliton Solutions Arising in Some NLEEs”, Bitlis Eren University Journal of Science and Technology, c. 12, sy. 1, ss. 51–59, 2022, doi: 10.17678/beuscitech.1115396.