Results 21 to 30 of about 327 (166)

Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation

Open Physics, 2021
The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field.
Seadawy Aly R., Rizvi Syed Tahir Raza, Ahmad Sarfraz, Younis Muhammad, Baleanu Dumitru   +4 more
doaj   +1 more source

Bilinear form of the regularized long wave equation and its multi-soliton solutions

Partial Differential Equations in Applied Mathematics, 2022
We consider utmost significant model, namely, the regularized long-wave equation involving dispersion and weedy nonlinearity effects that arises in the nonlinear dynamics of phonon packets in crystals, shallow water, plasma and ion acoustic waves.
Mohammad Mobarak Hossain, Harun-Or-Roshid, Md. Abu Naim Sheikh   +2 more
doaj   +1 more source

Multiple rogue wave and multiple lump solutions of a (3+1)-dimensional Korteweg-de Vries equation

上海师范大学学报. 自然科学版, 2021
Based on the Hirota bilinear form, we obtained the multiple rogue wave and multiple lump solutions of a new (3+1)-dimensional Korteweg-de Vries (KdV) equation.
TIAN Hongfei, SUN Yanfang, ZHANG Huiqun
doaj   +1 more source

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms [PDF]

Journal of Differential Equations, 2018
Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A
Wen-Xiu Ma, Yuan Zhou
openaire   +3 more sources

Line-soliton, lump and interaction solutions to the (2+1)-dimensional Hirota-Satsuma-Ito equation with time-dependent via Hirota bilinear forms

Results in Physics, 2023
In this paper, we consider the (2+1)-dimensional generalized Hirota-Satsuma-Ito equation with time-dependent, which has applications in describing the propagation of shallow water waves. Based on the bilinear formalism and with the aid of symbolic computation, we obtain line-soliton, lump, one-lump-one-stripe and one-lump-one-soliton using various ...
Deniu Yang, Xujie Jiang
openaire   +2 more sources

Construction of lump soliton and mixed lump stripe solutions of (3+1)-dimensional soliton equation

Results in Physics, 2018
In this letter, we apply two different ansatzs for constructing the lump soliton and mixed lump strip solutions of (3+1)-dimensional soliton equation, which is associating with the Hirota bilinear form.
Jiangen Liu, Yufeng Zhang
doaj   +1 more source

A novel and efficient method for obtaining Hirota’s bilinear form for the nonlinear evolution equation in (n+1) dimensions

Partial Differential Equations in Applied Mathematics, 2022
Bilinearization of nonlinear partial differential equations (PDEs) is essential in the Hirota method, which is a widely used and robust mathematical tool for finding soliton solutions of nonlinear PDEs in a variety of fields, including nonlinear dynamics, mathematical physics, and engineering sciences.
Sachin Kumar, Brij Mohan
openaire   +2 more sources

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

Hirota bilinear forms of the AKNS($N$) systems

, 2020
We study the AKNS($N$) hierarchy for $N=3,4,5,6$. We give the Hirota bilinear forms of these systems and present local and nonlocal reductions of them. We give the Hirota bilinear forms of the reduced equations. The compatibility of the commutativity diagrams of the application of the recursion operator, reductions of the AKNS($N$) systems, and Hirota ...
Gürses, Metin, Pekcan, Aslı
openaire   +2 more sources

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
openaire   +2 more sources