Results 11 to 20 of about 8,902 (211)

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   +3 more sources

Soliton fission and fusion of a new two-component Korteweg–de Vries (KdV) equation

Computers & Mathematics with Applications, 2011
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Yong, Xuelin, Yang, Yongping, Chen, Degang   +2 more
openaire   +3 more sources

Painlevé integrability and multiple soliton solutions for the extensions of the (modified) Korteweg-de Vries-type equations with second-order time-derivative

Alexandria Engineering Journal
This work introduces two (3+1)-dimensional expansions of the Korteweg–de Vries (KdV) and modified KdV (mKdV) equations. These extensions incorporate a second-order time-derivative term, similar to the Boussinesq equation. The Painlevé test is utilized to
Abdul-Majid Wazwaz, Weaam Alhejaili, R.T. Matoog, S.A. El-Tantawy   +3 more
doaj   +3 more sources

Analytical and Numerical Computations of Multi-Solitons in the Korteweg-de Vries (KdV) Equation [PDF]

Applied Mathematics, 2020
In this paper, an analytical and numerical computation of multi-solitons in Korteweg-de Vries (KdV) equation is presented. The KdV equation, which is classic of all model equations of nonlinear waves in the soliton phenomena, is described. In the analytical computation, the multi-solitons in KdV equation are computed symbolically using computer ...
Hycienth O. Orapine, Emem Ayankop-Andi, Godwin J. Ibeh   +2 more
openaire   +1 more source

A numerical solution of time-fractional coupled Korteweg-de Vries equation by using spectral collection method

Ain Shams Engineering Journal, 2018
In this paper, we present a numerical method proficient for solving a system of time–fractional partial differential equations. For this sake, we use spectral collection method based on shifted Chebyshev polynomials in space and finite difference method ...
Basim Albuohimad, Hojatollah Adibi, Saeed Kazem   +2 more
doaj   +1 more source

Hypercomplex Systems and Non-Gaussian Stochastic Solutions with Some Numerical Simulation of χ-Wick-Type (2 + 1)-D C-KdV Equations

Axioms, 2022
In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product.
Mohammed Zakarya, Mahmoud A. Abd-Rabo, Ghada AlNemer   +2 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

Modified homotopy perturbation method and its application to analytical solitons of fractional-order Korteweg–de Vries equation

Beni-Suef University Journal of Basic and Applied Sciences, 2022
Background Experimentally brought to light by Russell and hypothetically explained by Korteweg–de Vries, the KDV equation has drawn the attention of several mathematicians and physicists because of its extreme substantial structure in describing ...
Adedapo Ismaila Alaje, Morufu Oyedunsi Olayiwola, Kamilu Adewale Adedokun, Joseph Adeleke Adedeji, Asimiyu Olamilekan Oladapo   +4 more
doaj   +1 more source

The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation

Axioms, 2023
In this paper we consider examples of complex expansion (cKdV) and perturbation (pKdV) of the Korteweg–de Vries equation (KdV) and show that these equations have a representation in the form of the zero-curvature equation.
Tatyana V. Redkina, Arthur R. Zakinyan, Robert G. Zakinyan   +2 more
doaj   +1 more source

Second Order Scheme For Korteweg-De Vries (KDV) Equation

Journal of Bangladesh Academy of Sciences, 2019
The kinematics of the solitary waves is formed by Korteweg-de Vries (KdV) equation. In this paper, a third order general form of the KdV equation with convection and dispersion terms is considered. Explicit finite difference schemes for the numerical solution of the KdV equation is investigated and stability condition for a first-order scheme using ...
Laek Sazzad Andallah, Khandaker Md Eusha Bin Hafiz   +1 more
openaire   +2 more sources