Results 171 to 180 of about 3,184 (198)
Some of the next articles are maybe not open access.
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
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
2008We 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
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
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
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
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
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
Novel soliton solutions of CNLSEs with Hirota bilinear method
Journal of Optics, 2023openaire +1 more source
Physics Letters A
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
C.E. Nkenfack +3 more
openaire +2 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
C.E. Nkenfack +3 more
openaire +2 more sources
Physics Letters, Section A: General, Atomic and Solid State Physics, 2022
Shabir Ahmad, Mustafa Inc
exaly
Shabir Ahmad, Mustafa Inc
exaly
Hirota Bilinear Performance on Hirota–Satsuma–Ito Equation Using Bilinear Neural Network Method
International Journal of Applied and Computational MathematicsNguyen Minh Tuan, Nguyen Hong Son
openaire +1 more source