Results 21 to 30 of about 3,238 (183)
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 +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
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
Degenerate Four Virtual Soliton Resonance for KP-II [PDF]
, 2004 By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional Kadomtsev-Petviashvili (KP-II) equation is proposed.
B. Konopelchenko +10 more
core +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
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 +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
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
openaire +2 more sources
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 +4 more
doaj +1 more source
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