Results 171 to 180 of about 697 (208)

Hirota's Bilinear Method and its Generalization

International Journal of Modern Physics A, 1997
We review Hirota's bilinear method for constructing multisoliton solutions, its use in searching for new soliton equations, and its generalization to higher multi-linearity using gauge invariance as the determining property. Hirota's method is relevant even when a soliton solution is not the object of the study, as an example we show how it clarifies ...
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Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method

Physical Review E, 2008
The soliton interaction is investigated based on solving the higher-order nonlinear Schrödinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. By using Hirota's bilinear method, the analytic one-, two-, and three-soliton solutions of this model are obtained.
Wen-Jun, Liu, Bo, Tian, Hai-Qiang, Zhang, Li-Li, Li, Yu-Shan, Xue   +4 more
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Soliton Solutions of Coupled KdV System from Hirota's Bilinear Direct Method

Communications in Theoretical Physics, 2008
With Hirota's bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges
Yang Jian-Rong, Mao Jie-Jian
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The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq—Burgers equation

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.
Jin-Ming Zuo, Yao-Ming Zhang
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Novel interaction solutions to the (3+1)-dimensional Hirota bilinear equation by bilinear neural network method

Modern Physics Letters B
Solving differential equations is an ancient and very important research topic in theory and practice. The exact analytical solution to differential equations can describe various physical phenomena such as vibration and propagation wave. In this paper, the bilinear neural network method (BNNM), which uses neural network to unify all kinds of ...
Wenbo Ma, Sudao Bilige
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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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Hirota bilinear method for nonlinear evolution equations

2003
Summary. The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples including the Korteweg-deVries, nonlinear Schrodinger and Toda equations are given to show how solutions are derived.
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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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Collision of dust ion acoustic multisolitons in a non-extensive plasma using Hirota bilinear method

Physics of Plasmas, 2017
The collision of two, four, and six dust ion acoustic solitons (DIASs) in an unmagnetized non-extensive plasma is studied. The dispersion characteristics are analyzed. Using the extended Poincaré-Lighthill-Kue method, two different Korteweg–de Vries (KdV) equations are derived for the colliding DIASs.
S. K. El-Labany, W. F. El-Taibany, E. E. Behery, S. M. Fouda   +3 more
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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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