Results 21 to 30 of about 468 (168)

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

, 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 ...
Yokus, Asif, Isah, Muhammad Abubakar
core   +1 more source

A bilinear approach to a Pfaffian self-dual Yang-Mills equation [PDF]

, 2001
By using the bilinear technique of soliton theory, a pfaffian version of the SU(2) self-dual Yang-Mills equation and its solution is ...
Gilson, C.R., Ohta, Y., Nimmo, J.J.C.
core   +1 more source

Prolongation Structure of the KdV Equation in the Bilinear Form of Hirota [PDF]

, 1990
. The prolongation structure of the KdV equation in the bilinear form of Hirota is determined, the resulting Lie algebra is realised and the Backlund transformation obtained from the prolongation structure is derived.
R Martini, Martini, Ruud, Roelofs, Marcel, G H M Roelofs   +3 more
core   +1 more source

Dynamics of multi-solitons, multi-lumps and hybrid solutions in (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Results in Physics, 2022
The (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani (KdVSKR) equation is proposed by extending one dimension of the (1+1)-dimensional KdVSKR equation.
Chen Zhu, Chun-Xiao Long, Yi-Ting Zhou, Peng-Fei Wei, Bo Ren, Wan-Li Wang   +5 more
doaj   +1 more source

N-lump and interaction solutions of localized waves to the (2 + 1)-dimensional generalized KP equation

Results in Physics, 2021
With the aid of the binary Hirota polynomial scheme, the bilinear form of the generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation, is constructed.
Haixia Zhang, Jalil Manafian, Gurpreet Singh, Onur Alp Ilhan, Angelina Olegovna Zekiy   +4 more
doaj   +1 more source

Vector Shock Soliton and the Hirota Bilinear Method

, 2005
The Hirota bilinear method is applied to find an exact shock soliton solution of the system reaction-diffusion equations for n-component vector order parameter, with the reaction part in form of the third order polynomial, determined by three distinct ...
Pashaev, Oktay, Tanoğlu, Gamze
core   +2 more sources

Solitone solutions complexifications of the Korteweg - de Vriz equation

Наука. Инновации. Технологии, 2022
The Hirota method for construction of soliton solutions is applied to the complexification of the Korteweg-de Vries equation. To use the method, the complex equation is replaced by a system of two third-order equations into two real functions, which ...
Tatyana Valentinovna Redkina
doaj  

A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI. [PDF]

, 2018
We present some observations on the tau-function for the fourth Painle v ́e equation. By considering a Hirota bilinear equation of order four for this tau-function, we describ e the general form of the Taylor expansion around an arbitrary movable ze ro ...
A. N. W. Hone, Zullo, F., zullo, federico, F. Zullo, Hone, ANW, Hone, Andrew N.W.   +5 more
core   +1 more source

A Mathematical Study of the (3+1)-D Variable Coefficients Generalized Shallow Water Wave Equation with Its Application in the Interaction between the Lump and Soliton Solutions

Mathematics, 2022
In this paper, the Hirota bilinear method, which is an important scheme, is used. The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes of rational
Ruijuan Li, Onur Alp İlhan, Jalil Manafian, Khaled H. Mahmoud, Mostafa Abotaleb, Ammar Kadi   +5 more
doaj   +1 more source

Novel physical nonlinear structures in Saturn’s magnetosphere: Ion-acoustic solitons, lumps, and horseshoe-like nonlinear waves [PDF]

AIP Advances
In this paper, new analytical physical solutions to the Kadomtsev–Petviashvili–Bergers’ (KPB) equation in the multicomponent plasmas of Saturn are reported.
Weaam Alhejaili, Omer A. O. Gassim, Reda E. Tolba   +2 more
doaj   +1 more source