Results 21 to 30 of about 155 (137)

Different lump k-soliton solutions to (2+1)-dimensional KdV system using Hirota binary Bell polynomials

Open Physics, 2023
In this article, the (2+1)-dimensional KdV equation by Hirota’s bilinear scheme is studied. Besides, the binary bell polynomials and then the bilinear form is created.
Wu Xingxing, Manafian Jalil, Singh Gurpreet, Eslami Baharak, Aldurayhim Abdullah, Mohammad Ali khalil Noor Alhuda, Alawadi Ahmed   +6 more
doaj   +1 more source

Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation

Mathematics, 2023
A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N-soliton solutions are obtained using Hirota’s bilinear method.
Jian Zhang, Juan Yue, Zhonglong Zhao, Yufeng Zhang   +3 more
doaj   +1 more source

Bilinearization and new multi-soliton solutions of mKdV hierarchy with time-dependent coefficients

Open Physics, 2016
In this paper, Hirota’s bilinear method is extended to a new modified Kortweg–de Vries (mKdV) hierarchy with time-dependent coefficients. To begin with, we give a bilinear form of the mKdV hierarchy. Based on the bilinear form, we then obtain one-soliton,
Zhang Sheng, Zhang Luyao
doaj   +1 more source

Lump solution and lump-type solution to a class of water wave equation

Results in Physics, 2023
In the field of nonlinear sciences, the theory of solitons has long been regarded as one of the most significant and effective areas of research. In this research field, there are many efficient techniques for solving partial differential equations.
S. Liu, Z. Yang, A. Althobaiti, Y. Wang
doaj   +1 more source

The N-soliton molecule for the combined (2N+1)th-order Lax’s KdV equation

Results in Physics, 2020
Using the Hirota’s bilinear method combined with the velocity resonance mechanism, the two-soliton molecule, the three-soliton molecule and the four-soliton molecule for the third-fifth-order Lax’s KdV equation, the third-fifth-seventh-order Lax’s KdV ...
Xueping Cheng, Senyue Lou, Yunqing Yang, Peng Li, Shengwen Qi   +4 more
doaj   +1 more source

New lump solutions of the (3+1)-dimensional generalized Camassa–Holm Kadomtsev–Petviashvili (gCH-KP) equation

Results in Physics
In this paper, we investigate lump solutions of the (3+1)-dimensional gCH-KP equation employing the Hirota’s bilinear method and symbolic computation method.
Bin He
doaj   +1 more source

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

Complexity, 2020
We investigate a reduced generalized (3 + 1)-dimensional shallow water wave equation, which can be used to describe the nonlinear dynamic behavior in physics. By employing Bell’s polynomials, the bilinear form of the equation is derived in a very natural
Jing Wang, Biao Li
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,
Sachin Kumar, Brij Mohan
doaj   +1 more source

The symmetric breathers and lumps of the Boussinesq equation using the Alice–Bob transformation and Hirota’s bilinear derivative method

Results in Physics, 2023
Many two-place physical problems can be explicitly presented as related events model named Alice–Bob systems. In this paper, an integrable Alice–Bob Boussinesq system is introduced via the Boussinesq equation with parameters, which may meet the symmetry ...
Li-Hong Jiang, Hong-Yu Wu, Peng Dong, Zheng-Yi Ma   +3 more
doaj   +1 more source

Uncertainty Quantification of Analytical Solutions for the Nonlinear Space and Time Fractional Order ϕ4$$ {\phi}^4 $$ Equation Under Fuzziness

Engineering Reports, Volume 8, Issue 7, July 2026.
Analytical fuzzy soliton solutions of a modified space–time fractional ϕ4$$ {\phi}^4 $$ model are derived using EHFM, capturing memory effects and uncertainty. Results reveal diverse wave structures and show how fractional order and fuzziness significantly influence soliton amplitude, localization, and propagation, with heightened sensitivity near the ...
Mohsin Khalid, Neha Andaleeb Khalid, Baboucarr Ceesay, Zafar Iqbal   +3 more
wiley   +1 more source