Results 151 to 160 of about 3,238 (183)

An implementation for the algorithm of Hirota bilinear form of PDE in the Maple system

Applied Mathematics and Computation, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhou, Zhen-Jiang, Fu, Jing-Zhi, Li, Zhi-Bin   +2 more
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Stability analysis and solutions of (2 + 1)-Kadomtsev–Petviashvili equation by homoclinic technique based on Hirota bilinear form

Nonlinear Dynamics, 2022
Asif Yokus, Muhammad Abubakar Isah
openaire   +3 more sources

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

International Journal of Nonlinear Sciences and Numerical Simulation, 2022
Abstract 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 direct symbolic computation with Maple.
Melike Kaplan, Nauman Raza
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Lump solutions to a (2+1)-dimensional fourth-order nonlinear PDE possessing a Hirota bilinear form

Modern Physics Letters B, 2021
Through the Hirota bilinear formulation, a (2+1)-dimensional combined fourth-order nonlinear equation is proposed, which possesses lump solutions. Two classes of lump solutions are presented explicitly in terms of the coefficients in the combined nonlinear equation.
Wen-Xiu Ma, Solomon Manukure, Hui Wang, Sumayah Batwa   +3 more
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HIROTA BILINEAR FORM FOR THE SUPER-KdV HIERARCHY

Modern Physics Letters A, 1993
The integrability of the super-KdV hierarchy suggests that it can be written in Hirota bilinear form as the group orbit equation for some infinite-dimensional Lie algebra. We show how the first few equations in the hierarchy can be written in Hirota bilinear form.
McArthur, I. N., Yung, C. M.
openaire   +1 more source

Stability Analysis and Soliton Solutions of the Nonlinear Evolution Equation by Homoclinic Technique Based on Hirota Bilinear Form

2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), 2023
The novel KdV model plays a significant part in the discovery of a variety of nonlinear ion acoustic wave and harmonic crystal phenomena. The new homoclinic method based on the Hirota bilinear form is used to create the bilinear form of the new KdV equation and uncover numerous new exact solu tions.
Yokus, Asif, Isah, Muhammad Abubakar
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Bilinear forms and solitonic stability for a variable-coefficient Hirota-Satsuma coupled Korteweg-de Vries system in a liquid

Physics Letters A, 2023
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Yu-Qi Chen, Bo Tian, Cheng-Cheng Wei, Dan-Yu Yang   +3 more
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HBFTrans2: A Maple Package to Construct Hirota Bilinear Form for Nonlinear Equations

Communications in Theoretical Physics, 2011
An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D operator. The software package HBFTrans2 is written in Maple and its running efficiency is tested by a variety of soliton equations.
Xu-Dong Yang, Hang-Yu Ruan
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Rogue waves and Stability Analysis of the new (2+1)-KdV Equation Based on Symbolic Computation Method via Hirota Bilinear Form

2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), 2023
In this article, we study the novel KdV model which makes a significant contribution to the understanding of a variety of nonlinear occurrences of ion-acoustic waves in plasma and acoustic waves in harmonic crystals. Hirota bilinearization will be used to carry out the task via the proper transformations.
Muhammad Abubakar Isah, Asıf Yokus
openaire   +3 more sources

A Maple Package on Symbolic Computation of Hirota Bilinear Form for Nonlinear Equations

Communications in Theoretical Physics, 2009
An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations with logarithmic transformations is presented. In the algorithm, the general assumption of Hirota bilinear form is successfully reduced based on the property of uniformity in rank.
Yang Xu-Dong, Ruan Hang-Yu
openaire   +1 more source