Results 41 to 50 of about 12,223,520 (196)

A new study of soliton solutions for the variable coefficients Caudrey–Dodd–Gibbon equation

Journal of Taibah University for Science, 2022
We present a paper on the different methods for finding solutions to the Caudrey–Dodd–Gibbon equation with variable coefficients, which has wide applications in quantum mechanics and nonlinear optics.
Qinglian Yin, Ben Gao
doaj   +1 more source

Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches

Journal of Ocean Engineering and Science, 2023
By taking advantage of three different computational analytical methods: the Lie symmetry analysis, the generalized Riccati equation mapping approach, and the modified Kudryashov approach, we construct multiple new analytical soliton solutions to the ...
Shoukry El-Ganaini, Sachin Kumar, Monika Niwas   +2 more
doaj   +1 more source

Generalized Kudryashov Method for Time-Fractional Differential Equations [PDF]

, 2014
In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation.
Yusuf Pandir, Seyma Tuluce Demiray, Hasan Bulut   +2 more
core   +1 more source

New soliton wave solutions of a (2 + 1)-dimensional Sawada-Kotera equation

Journal of Ocean Engineering and Science, 2023
In this work, we studied a (2 + 1)-dimensional Sawada-Kotera equation (SKE). This model depicts nonlinear wave processes in shallow water, fluid dynamics, ion-acoustic waves in plasmas and other phenomena.
Kong Debin, Hadi Rezazadeh, Najib Ullah, Javad Vahidi, Kalim U. Tariq, Lanre Akinyemi   +5 more
doaj   +1 more source

The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

, 2023
In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger equations defined by Atangana’s conformable derivative using the general Kudryashov method. Firstly, Atangana’s conformable fractional derivative and its properties are
Gurefe, Yusuf
core   +1 more source

Construction of Analytical Solutions to the Conformable New (3+1)-Dimensional Shallow Water Wave Equation

Journal of New Theory, 2023
This study investigates the new (3+1)-dimensional shallow water wave equation. To do so, the definitions of conformable derivatives and their descriptions are given.
Mehmet Şenol, Mehmet Gençyiğit
doaj   +1 more source

Effective computational schemes for a mathematical model of relativistic electrons arising in the laser thermonuclear fusion

Results in Physics, 2020
This research paper investigates the computational wave solutions of the nonlinear Klein–Fock–Gordon (KFG) equation by applying two effective recent computational schemes. The nonlinear KFG model is a quantized version of the relativistic energy–momentum
Mostafa M.A. Khater, Mohamed S. Mohamed, Choonkil Park, Raghda A.M. Attia   +3 more
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Exact Solutions to Some Nonlinear Time-Fractional Evolution Equations Using the Generalized Kudryashov Method in Mathematical Physics [PDF]

, 2023
In this study, we utilize the potent generalized Kudryashov method to address the intricate obstacles presented by fractional differential equations in the field of mathematical physics.
Ekici, Mustafa, Mustafa Ekici
core   +1 more source

Abundant Wave Accurate Analytical Solutions of the Fractional Nonlinear Hirota–Satsuma–Shallow Water Wave Equation

Fluids, 2021
This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable fractional derivative is employed to convert the fractional system into a system with an integer–order.
Chen Yue, Dianchen Lu, Mostafa M. A. Khater   +2 more
doaj   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source