Results 21 to 30 of about 11,033,514 (203)

Construction of complexiton-type solutions using bilinear form of Hirota-type

, 2022
In this paper, based on the Hirota bilinear form and the extended transformed rational function method, complexiton solutions have been found of the Hirota–Satsuma–Ito (HSI) equation and generalized Calogero–Bogoyavlenskii–Schiff equation through a ...
Kaplan, Melike, Raza, Nauman
core   +1 more source

Hirota derivatives and representation theory [PDF]

, 2001
It is shown that the Hirota derivative can be used to construct the plethysm for tensor products of representations of {sl}_2(k)
Athorne, C.
core   +1 more source

Bäcklund Transformation and Exact Solutions to a Generalized (3 + 1)-Dimensional Nonlinear Evolution Equation

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
doaj   +1 more source

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
doaj   +1 more source

Linear Subspaces of Solutions Applied to Hirota Bilinear Equation [PDF]

, 2012
Linear subspace of solution is applied to Boussinesq and Kadomtseve-Petviashvili (KP) equations using Hirota bilinear transformation. A sufficient and necessary condition for the existence of linear subspaces of exponential travelling wave solutions to ...
M. Y. Adamu, Adamu, M. Y. (M), E. Suleiman, Suleiman, E. (E), Adamu, M. Y., Suleiman, E.   +5 more
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Dynamics of multi-solitons, multi-lumps and hybrid solutions in (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

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, Chun-Xiao Long, Yi-Ting Zhou, Peng-Fei Wei, Bo Ren, Wan-Li Wang   +5 more
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Construction of multi-wave complexiton solutions of the Kadomtsev-Petviashvili equation via two efficient analyzing techniques

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, Tukur Abdulkadir Sulaiman, E.M. Khalil, Mustafa Bayram, Hijaz Ahmad   +4 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 \(f_i\to e^{a\cdot x} f_i\).
openaire   +2 more sources