Results 71 to 80 of about 327 (166)

Constructing Physical Breather Solutions for the (2 + 1)‐ and (3 + 1)‐Dimensional Extended KdV and KP Systems via the Hirota Bilinear Method

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper presents an analysis of breather soliton solutions of the integrable extended KdV and KP equations in (2 + 1)‐ and (3 + 1)‐dimensional settings. Employing symbolic computation along with Hirota’s bilinear formalism, we construct positive logarithmic function solutions for the corresponding bilinear equations associated with each model. These
Ali Danladi, Ulviye Demirbilek, Taha Radwan, Karim K. Ahmed, Smritijit Sen   +4 more
wiley   +1 more source

Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation

Complexity, 2019
In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton
Baoyong Guo, Huanhe Dong, Yong Fang
doaj   +1 more source

Dynamic Behavior of the Chavy–Waddy–Kolokolnikov (CWK) Model of Bacterial Clustering in Phototaxis

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this study, we investigate the nonlinear dynamics of the continuity‐based Chavy–Waddy–Kolokolnikov (CWK) model for bacterial clustering in phototaxis. The model describes microorganism movement and pattern formation under light stimuli and thus serves as a useful prototype for biological transport processes.
Loubna Ouahid, Dhafer O. Alshahrani, M. A. Abdou, M. Ali Akbar, Smritijit Sen   +4 more
wiley   +1 more source

Unification of integrable q-difference equations

Electronic Journal of Differential Equations, 2015
This article presents a unifying framework for q-discrete equations. We introduce a generalized q-difference equation in Hirota bilinear form and develop the associated three-q-soliton solutions which are described in polynomials of power functions ...
Burcu Silindir, Duygu Soyoglu
doaj  

Rational Localized Waves and Their Absorb-Emit Interactions in the (2 + 1)-Dimensional Hirota–Satsuma–Ito Equation

Mathematics, 2020
In this paper, we investigate the (2 + 1)-dimensional Hirota–Satsuma–Ito (HSI) shallow water wave model. By introducing a small perturbation parameter ϵ, an extended (2 + 1)-dimensional HSI equation is derived.
Yuefeng Zhou, Chuanjian Wang, Xiaoxue Zhang   +2 more
doaj   +1 more source

The Dynamical Landscape of the Negative‐Order (3+1)‐Dimensional Calogero–Bogoyavlenskii–Schiff Equation

Journal of Mathematics, Volume 2026, Issue 1, 2026.
A new negative‐order form of the (3 + 1)‐dimensional Calogero–Bogoyavlenskii–Schiff equation is examined in this investigation. This equation plays an important role in accurately describing the thermodynamic properties of mixtures, particularly in chemical engineering applications.
Ulviye Demirbilek, Jan Muhammad, Arzu Akbulut, Usman Younas, Taha Radwan, Karim K. Ahmed, Dimitri Mugnai   +6 more
wiley   +1 more source

Dynamical Analysis of Wave Solutions for the Complex Ginzburg−Landau and (4 + 1)‐Dimensional Fokas Equations With Beta Derivative

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study propounds a detailed report on the exact wave solutions of the complex fractional Ginzburg−Landau equation (CFGLE) with quadratic‐cubic law nonlinearity and (4 + 1)‐dimensional fractional Fokas equation (FFE). For this purpose, the aforementioned equations are transformed into nonlinear ordinary differential equations (NLODEs) within the ...
Özlem Kırcı, Yusuf Pandır, Yusuf Gurefe, Hussain Juya, Yongqiang Fu   +4 more
wiley   +1 more source

Analyzing Soliton Solutions of the (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: Comprehensive study of dark, bright, and periodic dynamics

Results in Physics
This paper investigates the (n+1) dimensional integrable extension of the Kadomtsev–Petviashvili (KP) equation. The study focuses on extracting Auto-Bäcklund transformations for the given model using the extended homogeneous balance (HB) method in ...
Nauman Raza, Ahmed Deifalla, Beenish Rani, Nehad Ali Shah, Adham E. Ragab   +4 more
doaj   +1 more source

Abundant Symmetry-Breaking Solutions of the Nonlocal Alice–Bob Benjamin–Ono System

Complexity, 2020
The Benjamin–Ono equation is a useful model to describe the long internal gravity waves in deep stratified fluids. In this paper, the nonlocal Alice–Bob Benjamin–Ono system is induced via the parity and time-reversal symmetry reduction. By introducing an
Wang Shen, Zheng-Yi Ma, Jin-Xi Fei, Quan-Yong Zhu, Jun-Chao Chen   +4 more
doaj   +1 more source

A comprehensive study of qualitative analysis and soliton dynamics related to kairat-II-X-type equation

Ain Shams Engineering Journal
Nonlinear evolution equations have been found to be useful in modeling complicated wave dynamics in a wide range of applications, including fluid dynamics, nonlinear optics, plasma physics, and other fields of applied sciences.
Fozia Bashir Farooq, Nauman Raza, Muhammad Shahbaz, Salman Ali, Mustafa Bayram   +4 more
doaj   +1 more source