Results 21 to 30 of about 27,126 (206)
Discrete Dynamics in Nature and Society, 2022 In this article, a generalized (3 + 1)-dimensional nonlinear evolution equation (NLEE), which can be obtained by a multivariate polynomial, is investigated. Based on the Hirota bilinear method, the N-soliton solution and bilinear Bäcklund transformation (
Yali Shen, Ying Yang
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Chinese Physics B, 2011 This paper studies the coupled Burgers equation and the high-order Boussinesq—Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton) solutions and multiple-singular-kink (soliton) solutions are derived for the two equations.
Zuo Jin-ming, Zhang Yao-ming
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Exact Solution of (4+1)-Dimensional Boiti–Leon–Manna–Pempinelli Equation
Advances in Mathematical Physics, 2023 Based on the Hirota bilinear method, using the heuristic function method and mathematical symbolic computation system, various exact solutions of the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation including the block kink wave solution, block ...
Qili Hao
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Exact solutions of the generalized (2+1)-dimensional shallow water wave equation
Results in Physics, 2022 In this paper, we construct abundant exact solutions of generalized (2+1)-dimensional shallow water wave equation via the Hirota bilinear method and test functions. We obtain exact interaction solutions, such as solitons, lump solutions and lump-periodic
Shan Yu, Lin Huang
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Spatial self-bending soliton phenomenon of (2+1) dimensional bidirectional Sawada-Kotera equation
Results in Physics, 2023 In this study, we delve into the phenomenon of spatial self-bending solitons within the context of the (2+1)-dimensional bidirectional Sawada-Kotera equation.
Jing Wang, Biao Li
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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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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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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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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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