Results 31 to 40 of about 3,184 (198)
Periodic solutions for systems of coupled nonlinear Schrödinger equations with three and four components [PDF]
, 2003 Periodic solutions of systems of coupled nonlinear Schrödinger equations (CNLS) was discussed. Hirota bilinear method and elliptic functions were used.
Chow, KW, Lai, DWC
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Results in Physics, 2022 The (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani (KdVSKR) equation is proposed by extending one dimension of the (1+1)-dimensional KdVSKR equation.
Chen Zhu +5 more
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Results in Physics, 2021 This study aims to investigate the (2 + 1)-dimensional Kadomtsev-Petviashvili equation via the three-waves method through the Hirota bilinear form and the Kudryashov’s method.
Abdullahi Yusuf +4 more
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Solitons of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions: Hirota bilinear method [PDF]
Theoretical and Mathematical Physics, 2007 15 pages, 1 figure, talk presented in Workshop `Nonlinear Physics IV: Theory and Experiment`, 22-30 June 2006, Gallipoli ...
Lee, Jyh Hao, Pashaev, Oktay
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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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Prolongation structure of the KdV equation in the bilinear form of Hirota [PDF]
, 1990 The prolongation structure of the KdV equation in the bilinear form of Hirota is determined, the resulting Lie algebra is realised and the Backlund transformation obtained from the prolongation structure is derived.
Martini, Ruud +2 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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