Results 91 to 100 of about 5,895,681 (193)

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

Exact Soliton Dynamics and Stability Analysis of a Fractional Order Coupled Wu‐Zhang System via a Generalized Riccati−Bernoulli−Bäcklund Approach

Journal of Mathematics, Volume 2026, Issue 1, 2026.
To investigate the fractional coupled Wu‐Zhang system analytically, this paper uses a hybrid generalized Riccati−Bernoulli sub‐ODE scheme and Bäcklund transformation to find the exact kink, antikink, and bright‐kink soliton solutions. The dynamical properties of these solutions are discussed using Hamiltonian formulation, phase‐portrait analysis, and ...
M. Mossa Al-Sawalha, Linda Alzaben, Asıf Yokus   +2 more
wiley   +1 more source

Exact Traveling Wave Solutions of a Fractional Nonlinear Korteweg–de Vries Equation With Spatiotemporal Interaction Terms via the Atangana–Baleanu Operator

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study investigates the dynamical behavior of a nonlinear Korteweg–de Vries (KdV) equation incorporating second‐order spatiotemporal interaction terms within the framework of the Atangana–Baleanu fractional operator. The proposed model provides a generalized mathematical description of nonlinear wave propagation in dispersive media with memory ...
Saviour Worlanyo Akuamoah, Smritijit Sen
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

Anisotropic (N+1)-dimensional generalizations of Korteweg-de Vries, Kadomtsev-Petviashvili and Boussinesq equations via Hirota Bilinear Forms

The generalizations are constructed systematically with each of the lower dimensional cases explored appropriately. The Hirota bilinear forms of the constructed generalized partial differential equations are then derived utilizing key bilinear form ...
Sharad Anirudh Jonnalagadda
core   +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

Shallow-Water Wave Dynamics: Butterfly Waves, X-Waves, Multiple-Lump Waves, Rogue Waves, Stripe Soliton Interactions, Generalized Breathers, and Kuznetsov–Ma Breathers

Fractal and Fractional
A nonlinear (3+1)-dimensional nonlinear Geng equation that can be utilized to explain the dynamics of shallow-water waves in fluids is given special attention.
Sarfaraz Ahmed, Ujala Rehman, Jianbo Fei, Muhammad Irslan Khalid, Xiangsheng Chen   +4 more
doaj   +1 more source

Exact solution of some nonlinear differential equations by Hirota method [PDF]

, 2005
Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2005Includes bibliographical references (leaves: 45-47)Text in English; Abstract: Turkish and Englishix,60 leavesThe Hirota Bilinear Method is applied to construct exact analytical one ...
Güçoğlu, Deniz Hasan
core   +1 more source

Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation

, 2020
A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans.
M. Aligoli, M. Eslami, J.G. Liu, K. Hosseini, M. Mirzazadeh   +4 more
core   +1 more source