Results 41 to 50 of about 314 (173)
Abstract and Applied Analysis, 2014 The bilinear form, bilinear Bäcklund transformation, and Lax pair of a (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived through Bell polynomials. The integrable constraint conditions on variable coefficients
Wen-guang Cheng, Biao Li, Yong Chen
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Journal of Mathematics, Volume 2026, Issue 1, 2026.The Hirota–Maccari (HM) system is a fundamental model in wave propagation that has been widely utilized to investigate complex nonlinear phenomena in nonlinear optics, optical communications, and mathematical physics. The HM system sheds light on critical insights into soliton dynamics, wave interactions, and other nonlinear effects.
Fei Li +4 more
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Heliyon, 2020 A bilinear form of the (2+1)-dimensional nonlinear Calogero–Bogoyavlenskii–Schiff (CBS) model is derived using a transformation of dependent variable, which contain a controlling parameter.
Harun-Or- Roshid +2 more
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Journal of Ocean Engineering and Science, 2023 The paper investigates the multiple rogue wave solutions associated with the generalized Hirota–Satsuma–Ito (HSI) equation and the newly proposed extended (3 + 1)-dimensional Jimbo–Miwa (JM) equation with the help of a symbolic computation technique.
Saima Arshed +4 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.A new negative‐order form of the (3 + 1)‐dimensional Calogero–Bogoyavlenskii–Schiff equation is examined in this investigation. This equation plays an important role in accurately describing the thermodynamic properties of mixtures, particularly in chemical engineering applications.
Ulviye Demirbilek +6 more
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Complexity, 2019 We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are ...
Shou-Ting Chen, Wen-Xiu Ma
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This study propounds a detailed report on the exact wave solutions of the complex fractional Ginzburg−Landau equation (CFGLE) with quadratic‐cubic law nonlinearity and (4 + 1)‐dimensional fractional Fokas equation (FFE). For this purpose, the aforementioned equations are transformed into nonlinear ordinary differential equations (NLODEs) within the ...
Özlem Kırcı +4 more
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Open Physics, 2022 In this work, a (2+1)-dimensional generalized Hirota–Satsuma–Ito equation realized to represent the propagation of unidirectional shallow water waves is investigated.
Zhang Yun-Xia, Xiao Li-Na
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Higher order Hirota bilinear forms
In this paper we study Hirota bilinear forms of the type $P(D) \{f\cdot f\}=0$. We prove that for $P(D)=D_x^mD_y^rD_t^n$ the equations have three-soliton solutions if only if two of nonzero $m,n,p$ are odd and the other one even. We explicitly derive the nonlinear partial differential equations corresponding to this form for $m+n+p=4$ and $m+n+p=6$. We
Gürses, Metin, Pekcan, Aslı
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Results in Physics, 2021 In this paper, Hirota’s bilinear form has been employed to find novel lump waves solutions for the generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation. This equation is one of the most widely used equations in the field of fluid mechanics. Using the employed technique in the paper, several different categories of solutions to the equation are ...
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