Results 31 to 40 of about 327 (166)

Some integrable maps and their Hirota bilinear forms

Journal of Physics A: Mathematical and Theoretical, 2017
We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the ...
A N W Hone, T E Kouloukas, G R W Quispel
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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
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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  

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
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Lump-Type and Bell-Shaped Soliton Solutions of the Time-Dependent Coefficient Kadomtsev-Petviashvili Equation

Frontiers in Physics, 2020
In this article, the lump-type solutions of the new integrable time-dependent coefficient (2+1)-dimensional Kadomtsev-Petviashvili equation are investigated by applying the Hirota bilinear technique and a suitable ansatz.
Aliyu Isa Aliyu, Yongjin Li, Liu Qi, Mustafa Inc, Dumitru Baleanu, Dumitru Baleanu, Ali S. Alshomrani   +6 more
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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
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The symmetry breaking solutions of the nonlocal Alice–Bob B-type Kadomtsev–Petviashvili system

Results in Physics, 2023
The (2+1)-dimensional B-type Kadomtsev–Petviashvili equation is an integrable model, which can be used to describe the shallow water wave in a fluid. In this paper, the nonlocal Alice–Bob B-type Kadomtsev–Petviashvili system is induced via the principle ...
Peng Dong, Zheng-Yi Ma, Hui-Ling Wu, Quan-Yong Zhu   +3 more
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Higher order Hirota bilinear forms

Journal of Physics: Conference Series
Abstract In this paper we study Hirota bilinear forms of the type P ( D
Gürses, Metin, Pekcan, Aslı
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Lump and Interaction Solutions to the (3+1)-Dimensional Variable-Coefficient Nonlinear Wave Equation with Multidimensional Binary Bell Polynomials

Journal of Function Spaces, 2021
In this paper, we study the (3+1)-dimensional variable-coefficient nonlinear wave equation which is taken in soliton theory and generated by utilizing the Hirota bilinear technique.
Xuejun Zhou, Onur Alp Ilhan, Fangyuan Zhou, Sutarto Sutarto, Jalil Manafian, Mostafa Abotaleb   +5 more
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New double Wronskian exact solutions for a generalized (2+1)-dimensional nonlinear system with variable coefficients

Partial Differential Equations in Applied Mathematics, 2021
New generalized (2+1)-dimensional Boussinesq system with variable coefficients has been introduced. A double Wronskian solutions has been formulated to the new system under certain constraints on the variable coefficients.
Alrazi Abdeljabbar
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