Results 71 to 80 of about 27,126 (206)

The bilinear neural network method for solving Benney–Luke equation

Partial Differential Equations in Applied Mathematics
Benney–Luke equation, the estimation of water wave propagation on the water’s surface, is significantly important in studying the tension of water waves in physics.
Nguyen Minh Tuan, Sanoe Koonprasert, Sekson Sirisubtawee, Phayung Meesad   +3 more
doaj   +1 more source

Optical Solitons and Analysis of Chaotic Nature for the Temporal M‐Fractional Yajima–Oikawa Model in Shortwave and Longwave

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study proposes a comprehensive study on fractional soliton solutions and chaotic nature for the temporal M‐fractional Yajima–Oikawa (YO) model in shortwave and longwave regimes. Utilizing the new Jacobian elliptic function method, the optical soliton solutions are examined with diverse categories, including kinky‐periodic wave, kink with bell wave,
Md. Mamunur Roshid, Mrityunjoy Kumar Pandit, Mahtab Uddin, Golam Mostafa, Harun-Or-Roshid, Pramita Mishra   +5 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  

A class of lump solutions and localized excitations for the generalized (3 + 1)-dimensional KP equation

Results in Physics, 2020
Based on symbolic computation and Hirota bilinear form, a class of lump solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation is given. As a result, the lump solution shows a new perspective to knowledge them. Meanwhile,
Ping Cui
doaj   +1 more source

On the Dispersive Optical Pulses in Fiber Optics of the Conformable (2 + 1)‐Dimensional Hirota–Maccari System

Journal of Mathematics, Volume 2026, Issue 1, 2026.
The Hirota–Maccari (HM) system is a fundamental model in wave propagation that has been widely utilized to investigate complex nonlinear phenomena in nonlinear optics, optical communications, and mathematical physics. The HM system sheds light on critical insights into soliton dynamics, wave interactions, and other nonlinear effects.
Fei Li, Mesut Balibey, Shafqat Ur Rehman, Muhammad Bilal, Smritijit Sen   +4 more
wiley   +1 more source

Complex wave phenomena in blood flow: Breather, rogue, and interaction solutions of a higher-order nonlinear Schrödinger equation

Results in Applied Mathematics
In this paper, we consider the study of nonlinear wave propagation in arterial blood flow through a higher-order nonlinear Schrödinger (HONLS) equation with nonlinear and higher-order dispersive effects.
Sheikh Zain Majid, Fatma Nur Kaya Sağlam, Abdulla Al Mamun   +2 more
doaj   +1 more source

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

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

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