Results 21 to 30 of about 394 (186)
Mathematics, 2022 In this paper, the Hirota bilinear method, which is an important scheme, is used. The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes of rational
Ruijuan Li +5 more
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Solitone solutions complexifications of the Korteweg - de Vriz equation
Наука. Инновации. Технологии, 2022 The Hirota method for construction of soliton solutions is applied to the complexification of the Korteweg-de Vries equation. To use the method, the complex equation is replaced by a system of two third-order equations into two real functions, which ...
Tatyana Valentinovna Redkina
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Results in Physics, 2021 In this work, we established some exact solutions for the (3 + 1)-dimensional potential-Yu-Toda-Sasa-Fukuyama (YTSF)-like equation with p=3 and p=5 which are considered based on the generalized Hirota bilinear method.
Lei Huang +4 more
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Introduction to the Hirota Bilinear Method [PDF]
, 2004 We give an elementary introduction to Hirota's direct method of constructing multisoliton solutions to integrable nonlinear evolution equations. We discuss in detail how this works for equations in the Korteweg-de Vries class. We also show how Hirota's method can be used to search for new integrable evolution equations by testing for the existence of 3-
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Gauge symmetry and the generalization of Hirota's bilinear method [PDF]
Journal of Nonlinear Mathematical Physics, 1996 The author discusses an extension of Hirota's bilinear formalism leading to any degree of multilinearity. The main guideline in this generalization is gauge-invariance: the original nonlinear equation should be transformed into a form that is invariant under a gauge transformation \(f_i\to e^{a\cdot x} f_i\).
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Novel physical nonlinear structures in Saturn’s magnetosphere: Ion-acoustic solitons, lumps, and horseshoe-like nonlinear waves [PDF]
AIP AdvancesIn this paper, new analytical physical solutions to the Kadomtsev–Petviashvili–Bergers’ (KPB) equation in the multicomponent plasmas of Saturn are reported.
Weaam Alhejaili +2 more
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Localized coherent structures of Ishimori equation I through Hirota’s bilinearization method: Time dependent/stationary boundaries [PDF]
Chaos, Solitons & Fractals, 2007 Ishimori equation is a $(2+1)$ dimensional generalization of the $(1+1)$ dimensional integrable classical continuous Heisenberg ferromagnetic spin equation. The richness of the coherent structures admitted by Ishimori equation I such as dromion, lump and rationally- exponentially localized solutions, have been demonstrated in the literature through ...
Vijayalakshmi, S., Lakshmanan, M.
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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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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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Shifted nonlocal Kundu type equations: Soliton solutions
Partial Differential Equations in Applied Mathematics, 2022 We study the shifted nonlocal reductions of the integrable coupled Kundu type system. We then consider particular cases of this system; namely Chen–Lee–Liu, Gerdjikov–Ivanov, and Kaup–Newell systems.
Aslı Pekcan
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