This article explores the solution of the regularized long-wave equation (RLWE) and modified RLWE (MRLWE) using a semi-analytical approach known as the homotopy perturbation transform method (HPTM), revealing the characteristics of shallow water waves and ion-acoustic plasma waves. The effectiveness and accuracy of the technique are demonstrated by solving scenarios involving a single solitary wave (SSW) and two solitary waves (TSW) presented and compared with the exact solution of the RLWE. Furthermore, we introduced a fuzzy model for both RLWE and MRLWE, considering uncertainties in the coefficients related to the wave amplitude, and to understand the behavior of both fuzzy RLWE (FRLWE) and fuzzy MRLWE (FMRLWE) in the SSW by examining various numerical results using MATLAB.
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Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China
Qufu Normal Univ, Sch Management, Rizhao 276800, Peoples R ChinaWeifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China
Pan, Xintian
Zhang, Luming
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Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R ChinaWeifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China
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Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, IranAmirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran
Dehghan, Mehdi
Salehi, Rezvan
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Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, IranAmirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran
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Qufu Normal Univ, Sch Management, Rizhao 276800, Shandong, Peoples R China
Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R ChinaQufu Normal Univ, Sch Management, Rizhao 276800, Shandong, Peoples R China
Pan, Xintian
Che, Haitao
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Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R ChinaQufu Normal Univ, Sch Management, Rizhao 276800, Shandong, Peoples R China
Che, Haitao
Wang, Yiju
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Qufu Normal Univ, Sch Management, Rizhao 276800, Shandong, Peoples R ChinaQufu Normal Univ, Sch Management, Rizhao 276800, Shandong, Peoples R China
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Henan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Henan, Peoples R China
Minnan Normal Univ, Sch Math & Stat, Zhangzhou 363000, Fujian, Peoples R ChinaHenan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Henan, Peoples R China
Wang, Xiaofeng
Dai, Weizhong
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Louisiana Tech Univ, Coll Engn & Sci, Math & Stat, Ruston, LA 71272 USAHenan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Henan, Peoples R China
Dai, Weizhong
Guo, Shuangbing
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Henan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Henan, Peoples R ChinaHenan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Henan, Peoples R China