Results 171 to 180 of about 27,126 (206)

Hirota’s Bilinear Method and Its Connection with Integrability

2008
We give an introduction to Hirota’s bilinear method, which is particularly efficient for constructing multisoliton solutions to integrable nonlinear evolution equations. We discuss in detail how the method works for equations in the Korteweg–de Vries class and then go through some other classes of equations.
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Hirota’s Bilinear Method and Partial Integrability

1990
We discuss Hirota’s bilinear method from the point of view of partial integrability. Many different levels of integrability are shown to exist.
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2 + 1 Dimensional Dromions and Hirota’s Bilinear Method

1991
Hirota’s bilinear formalism is perhaps the best method for constructing solutions of integrable nonlinear evolution equations [1,2]. In this lecture we show how using this method one can easily construct one-dromion solutions for generic equations of nonlinear Schrodinger (n1S) and Korteweg-de Vries (KdV) type [3,4].
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Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation

Nonlinear dynamics, 2023
Tianle Yin, Zhanqing Xing, J. Pang
semanticscholar   +1 more source

Extracted different types of optical lumps and breathers to the new generalized stochastic potential-KdV equation via using the Cole-Hopf transformation and Hirota bilinear method

Optical and quantum electronics, 2022
Rahaf Alhami, Marwan Alquran
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Construction of fractional granular model and bright, dark, lump, breather types soliton solutions using Hirota bilinear method

Chaos, Solitons & Fractals, 2023
Swapan Biswas, U. Ghosh, S. Raut
semanticscholar   +1 more source

Resonant multi-wave, positive multi-complexiton, nonclassical Lie symmetries, and conservation laws to a generalized Hirota bilinear equation

Modern physics letters B
This paper explores the evolutionary behavior of some specific waves for a Generalized Hirota Bilinear (GHB) equation with applications in modern sciences.
K. Hosseini, F. Alizadeh, E. Hinçal, D. Baleanu, M. S. Osman, A. Wazwaz   +5 more
semanticscholar   +1 more source

Constructing Quasi-Periodic Wave Solutions of Differential-Difference Equation by Hirota Bilinear Method

Zeitschrift für Naturforschung A, 2016
Abstract In the present paper, based on the Riemann theta function, the Hirota bilinear method is extended to directly construct a kind of quasi-periodic wave solution of a new integrable differential-difference equation. The asymptotic property of the quasi-periodic wave solution is analyzed in detail.
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Periodic solutions, breather, lump and interaction solutions of a generalized (2+1)-dimensional Hirota bilinear equation via the bilinear neural network method

Communications in Theoretical Physics
Abstract The main focus of this paper is to address a generalized (2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method. The paper presents the periodic solutions through a single-layer model of [3-4-1], followed by breather, lump and their interaction solutions by using double-layer models of [3-3-2-1 ...
Zhao, Zhao, Ren, Bo
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The nondegenerate solitons solutions for the vcGCNLS equations with four-wave mixing terms via the Hirota bilinear method

Physica Scripta
Abstract In this article, we delve into the variable coefficient generalized coupled nonlinear Schrödinger (vcGCNLS) equations with four-wave mixing terms in the context of a birefringent fiber, encompassing time-dependent diffraction, nonlinearity, and gain (loss) parameters.
Zilin Wang, Ben Gao
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