Results 61 to 70 of about 453 (182)

On abundant new solutions of two fractional complex models

Advances in Difference Equations, 2020
We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg–de Vries equation (KdV) equation and the fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation).
Mostafa M. A. Khater, Dumitru Baleanu
doaj   +1 more source

Kudryashov Expansion Method Applied to Fisher Mathematical Model

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
We obtain new computational soliton solutions characterized by topological, rational, exponential, trigonometric, and hyperbolic functions for the Fisher equation. Using a good strategy, the Kudryashov expansion method is used to find different dynamical wave structures of soliton solutions within the scope of evolutionary dynamical structures of ...
Elif Deniz Öztürk, Ercan Çelik, Sıdıka Şule Şener Kiliç, Kang-Jia Wang   +3 more
wiley   +1 more source

White-Noise-Driven KdV-Type Boussinesq System

Mathematics
The white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize features from both the ...
Aissa Boukarou, Safa M. Mirgani, Khaled Zennir, Keltoum Bouhali, Sultan S. Alodhaibi   +4 more
doaj   +1 more source

Numerical Simulations of Coupled Solitary Waves With Spatially Modulated Non‐Linearity

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This study investigates the dynamics of two coupled solitary waves propagating in media characterised by spatially modulated non‐linearity and variable dispersion. By employing numerical simulations of a system of coupled non‐linear Schrödinger equations (NLSEs) with varying coefficients, we analyse how inhomogeneous physical properties influence ...
Ngaka John Nchejane, Mabatho Thakedi, Shikha Binwal   +2 more
wiley   +1 more source

Parameter Estimation for Stochastic Korteweg–de Vries Equations

Axioms
In this paper, we propose two methods for parameter estimation in stochastic Korteweg–de Vries (KdV) equations with unknown parameters. Both methods are based on the numerical discretization of the stochastic KdV equation. Moreover, we further propose an
Zhenyu Lang, Xiuling Yin, Yanqin Liu, Yaru Wang   +3 more
doaj   +1 more source

Dynamical Behavior and Chaotic Nature of M‐Fractional Paraxial Wave Equation With Three Analytical Methods

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid, Mahtab Uddin, Mohammad Safi Ullah, Golam Mostafa, Ashek Ahmed, Shikha Binwal   +5 more
wiley   +1 more source

Constructing Traveling Wave Solutions via a Generalized Expansion Method for Nonlinear Evolution Equations Possessing Variable Coefficients

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended ...
Abdul Saboor, Xianhua Song, Muhammad Shakeel, Muhammad Qamar Fareed, Baboucarr Ceesay, Kang-Jia Wang   +5 more
wiley   +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

Error estimates for a physics-informed neural network in solving KdV equations

Machine Learning: Science and Technology
This paper aims to provide error bounds on physics-informed neural network (PINN) in solving Korteweg–de Vries (KdV) equations. We prove that a neural network equipped with two hidden layers and the tanh activation function can reduce the partial ...
Jia Guo, Ziyuan Liu, Chenping Hou
doaj   +1 more source

the Solving Partial Differential Equations by using Efficient Hybrid Transform Iterative Method

Tikrit Journal of Pure Science
The aim of this article is to propose an efficient hybrid transform iteration method that combines the homotopy perturbation approach, the variational iteration method, and the Aboodh transform forsolving various partial differential equations.
Ruaa Shawqi Ismael, Ali Al -Fayadh, Saad M. Salman   +2 more
doaj   +1 more source