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Two Mode Version of Hirota-Ramani Equation and its Abundant Soliton Structures | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 فروردین 1405 اصل مقاله (6.84 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.68527.3318 | ||
| نویسندگان | ||
| Ulviye Demirbilek1؛ Ali Danladi2؛ Hasan Bulut3؛ Imran Siddique* 4؛ Barno Abdullaeva5؛ Zaher M Yaseen6 | ||
| 1Department of Mathematics, Mersin University, Mersin, Turkey. | ||
| 2Department of Mathematics, Federal University, Dutse, Nigeria. | ||
| 3Department of Mathematics, Firat University, Elazığ, Turkey. | ||
| 41. Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan.\\ 2. Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah, 64001, Iraq. | ||
| 5Department of Mathematics and Information Technologies, Tashkent State Pedagogical University, Tashkent, Uzbekistan. | ||
| 6Civil and Environmental Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. | ||
| چکیده | ||
| Wave propagation phenomena are connected to Hirota-Ramani equation (HRE) and as a member of the integrable PDEs, the HRE is used in many different domains. Considering this, we employ Kursonky’s approach and developed the two-mode or Dual-mode version of the HRE that describes the propagation of two-wave solitons moving simultaneously in the same direction with mutual interaction that depends on an embedded phase-velocity parameter. The existing studies explore single mode version of HRE whereas two mode version remain unexplored. Motivated by this gap, we utilized the generalized Ricatti equation mapping method and the modified extended tanh-function method to find the different soliton structures of the developed model. By using these techniques we developed bright, dark, kink, anti-kink, singular and peakon shaped soliton solutions. Additionally, we performed a stability analysis of the LGH equation using the linear stability approach. A back substitution for each of the obtained result into the developed model was performed to ensure reliability and accuracy of the obtained solutions. The 3D and 2D graphical representation of some of the obtained results were portrayed. The efficacy and competence of the proposed methods in analyzing and obtaining soliton solutions for nonlinear partial differential equations (NLPDEs) are demonstrated through their implementation in this work. Additionally, the derived solutions are original and reflect contributions not previously documented in the literature. | ||
| کلیدواژهها | ||
| Hirota-Ramani-Equation؛ Two-mode models؛ Stability Analysis؛ Generalized Ricatti Equation Mapping Method؛ Modified Extended Tanh-Function Method | ||
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آمار تعداد مشاهده مقاله: 16 تعداد دریافت فایل اصل مقاله: 72 |
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