Results 141 to 150 of about 394 (186)

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
openaire   +1 more source

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.
openaire   +1 more source

Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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.
openaire   +1 more source

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].
openaire   +1 more source

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
openaire   +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.
openaire   +1 more source

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.
openaire   +1 more source

Multisoliton solutions of a (2+1)-dimensional variable-coefficient Toda lattice equation via Hirota’s bilinear method

Canadian Journal of Physics, 2014
In this paper, Hirota’s bilinear method is extended to construct multisoliton solutions of a (2+1)-dimensional variable-coefficient Toda lattice equation. As a result, new and more general one-soliton, two-soliton, and three-soliton solutions are obtained, from which the uniform formula of the N-soliton solution is derived.
Sheng Zhang, Dong Liu
openaire   +1 more source

Application of Hirota's Direct Method to Nonlinear Partial Differential Equations: Bilinear Form and Soliton Solutions

2022
The Hirota method to get the soliton solutions for a nonlinear partial differential equation is the mostefficient direct technique researchers use worldwide. This article reviews and explores Hirota’s directtechnique on the KdV equation, which Hirota initially used to clarify his method.
openaire   +1 more source