Results 51 to 60 of about 453 (182)

A Note on the Fractional Generalized Higher Order KdV Equation

Journal of Function Spaces, 2018
We obtain exact solutions to the fractional generalized higher order Korteweg-de Vries (KdV) equation using the complex method. It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations ...
Yongyi Gu
doaj   +1 more source

Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation

Advances in Mathematical Physics, 2022
Nonlinear evolution equations are crucial for understanding the phenomena in science and technology. One such equation with periodic solutions that has applications in various fields of physics is the Korteweg-de Vries (KdV) equation. In the present work,
Shubham Mishra, Geeta Arora, Homan Emadifar, Soubhagya Kumar Sahoo, Afshin Ghanizadeh   +4 more
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Traveling wave solutions of generalized seventh-order time-fractional KdV models through He-Laplace algorithm

Alexandria Engineering Journal, 2023
Non-linear evolution equations play a prominent role in describing a wide range of phenomena in optical fibers, fluid dynamics, electromagnetic radiation, plasma and solid state physics.
Mubashir Qayyum, Efaza Ahmad, Syed Tauseef Saeed, Ali Akgül, Muhammad Bilal Riaz   +4 more
doaj   +1 more source

Unitary ensembles with a critical edge point, their multiplicative statistics, and the Korteweg‐de‐Vries hierarchy

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We study the multiplicative statistics associated to the limiting determinantal point process describing eigenvalues of unitary random matrices with a critical edge point, where the limiting eigenvalue density vanishes like a power 5/2. We prove that these statistics are governed by the first three equations of the Korteweg‐de‐Vries (KdV ...
Mattia Cafasso, Carla Mariana da Silva Pinheiro   +1 more
wiley   +1 more source

Traveling Wave Solutions of Fractional Differential Equations Arising in Warm Plasma

مجلة بغداد للعلوم, 2023
This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free ...
Krishna Ghode, Kalyanrao Takale, Shrikisan Gaikwad   +2 more
doaj   +1 more source

Fractional Novel Analytical Method (FNAM): An Improved Innovative Numerical Scheme to Solve Fractional Differential‐Difference Equations

Engineering Reports, Volume 8, Issue 2, February 2026.
This paper introduces the Fractional Novel Analytical Method (FNAM), a Taylor‐series‐based technique for approximating nonlinear fractional differential‐difference equations. Built on the Caputo derivative, FNAM achieves rapid convergence without relying on Adomian polynomials, perturbation schemes, or transform methods.
Uroosa Arshad, Mariam Sultana, Homan Emadifar, Atul Kumar   +3 more
wiley   +1 more source

Numerical Analysis of a Benjamin–Bona–Mahony Type Equation in a Noncylindrical Domain

Mathematical Methods in the Applied Sciences, Volume 49, Issue 2, Page 818-834, 30 January 2026.
ABSTRACT Numerical analysis and simulation for the approximate solution of a Benjamin–Bona–Mahony type equation defined in a noncylindrical domain are presented in this article. The approximate problem is defined using the linearized Crank–Nicolson Galerkin method, which results in a linear algebraic system at each time step while maintaining quadratic
Vania Cristina Machado, Bruno Alves do Carmo, Mauro Antonio Rincon   +2 more
wiley   +1 more source

Weak asymptotic method for the study of propagation and interaction of infinitely narrow delta-solitons

Electronic Journal of Differential Equations, 2003
We present a new method for studying the interaction of solitons for non-integrable Korteweg-de Vries (KdV) type equations with small dispersion and test this method for the KdV equation.
Vladimir G. Danilov, Georgii A. Omel'yanov   +1 more
doaj  

The solution of fractional-order system of KdV equations with exponential-decay kernel

Results in Physics, 2022
This study uses efficient techniques to evaluate a non-linear system of Korteweg–de Vries (KdV) equations with fractional Caputo Fabrizio derivative, including the modified decomposition approach and the novel iterative transform method.
Mohammad Alshammari, Naveed Iqbal, Wael W. Mohammed, Thongchai Botmart   +3 more
doaj   +1 more source

Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation

Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.
ABSTRACT Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space‐time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave ...
Dmitry E. Pelinovsky, Rudi Weikard
wiley   +1 more source