Results 41 to 50 of about 8,881 (223)

Travelling wave solutions for fractional Korteweg-de Vries equations via an approximate-analytical method

AIMS Mathematics, 2019
This paper introduces an approximate-analytical method (AAM) for solving nonlinear fractional partial differential equations (NFPDEs) in full general forms.
Hayman Thabet, Subhash Kendre, James Peters   +2 more
doaj   +1 more source

Spatial Analyticity of Solutions to Korteweg–de Vries Type Equations

Mathematical and Computational Applications, 2021
The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces. It is given as third-order nonlinear partial differential equation and plays a very important role in the theory of nonlinear waves.
Keltoum Bouhali, Abdelkader Moumen, Khadiga W. Tajer, Khdija O. Taha, Yousif Altayeb   +4 more
doaj   +1 more source

Variable depth KDV equations and generalizations to more nonlinear regimes [PDF]

, 2008
We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced.
Alvarez-Samaniego, Alvarez-Samaniego, Benjamin, Bona, Bona, Camassa, Constantin, Craig, Green, Grimshaw, Iguchi, Johnson, Johnson, Korteweg, Lannes, Lannes, Lannes, Miles, Nalimov, Peregrine, Pudjaprasetya, Pudjaprasetya, Samer Israwi, Schneider, van Groesen, Well-posedness, Well-posedness, Yoon, Yosihara   +28 more
core   +4 more sources

Exact solutions of stochastic Burgers–Korteweg de Vries type equation with variable coefficients

Partial Differential Equations in Applied Mathematics
We will present exact solutions for three variations of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equation featuring variable coefficients.
Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo   +6 more
doaj   +1 more source

A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law

Journal of Mathematics, 2022
This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative.
Noufe H. Aljahdaly, Ali Akgül, Rasool Shah, Ibrahim Mahariq, Jeevan Kafle   +4 more
doaj   +1 more source

Review of Some Modified Generalized Korteweg–De Vries–Kuramoto–Sivashinsky (mgKdV-KS) Equations

Foundations
This paper reviews the results of existence and uniqueness of the solutions of these equations: the Korteweg–De Vries equation, the Kuramoto–Sivashinsky equation, the generalized Korteweg–De Vries–Kuramoto–Sivashinsky equation and the nonhomogeneous ...
Marie-Thérèse Aimar, Abdelkader Intissar   +1 more
doaj   +1 more source

Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations

Abstract and Applied Analysis, 2014
The modeling of unidirectional propagation of long water waves in dispersive media is presented. The Korteweg-de Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations are derived from water waves models.
A. R. Seadawy, A. Sayed
doaj   +1 more source

New numerical solutions of fractional-order Korteweg-de Vries equation

Results in Physics, 2020
We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving.
Mustafa Inc, Mohammad Parto-Haghighi, Mehmet Ali Akinlar, Yu-Ming Chu   +3 more
doaj   +1 more source

A Regularization-Free Scheme for Recovering Large External Forces of Higher-Order Nonlinear Evolution Equations

Axioms, 2023
In this study, the inverse engineering problems of the Ostrovsky equation (OE), Kawahara equation (KE), modified Kawahara equation (mKE), and sixth-order Korteweg-de Vries (KdV) equation will be investigated numerically.
Chih-Wen Chang
doaj   +1 more source

On a hierarchy of nonlinearly dispersive generalized KdV equations

, 2015
We propose a hierarchy of nonlinearly dispersive generalized Korteweg--de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. It is shown that two recent nonlinear
Christov, Ivan C.
core   +1 more source