Results 61 to 70 of about 18,045 (194)

Wronskians, Generalized Wronskians and Solutions to the Korteweg-de Vries Equation

, 2003
A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg-de Vries equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions.
Ma, Wen-Xiu
core   +2 more sources

Exploring the Chavy–Waddy–Kolokolnikov Model: Analytical Study via Recently Developed Techniques

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This work explores the analytical soliton solutions to the Chavy–Waddy–Kolokolnikov equation (CWKE), which is a well‐known equation in biology that shows how light‐attracted bacteria move together. This equation is very useful for analyzing pattern creation, instability regimes, and minor changes in linear situations since bacterial movement is very ...
Jan Muhammad, David Yaro, Usman Younas, Chang Phang   +3 more
wiley   +1 more source

ANALYSIS OF THE RESULTS OF COMPUTER SIMULATION N-SOLITON SOLUTIONS OF THE KORTEWEG – DE VRIES EQUATION

Informatika, 2017
The results of computer simulation N-soliton solutions of the Korteweg – de Vries equation with N = 1, 2, 3, 4 are shown. Using numerical experiment the property of conservation of area under the envelope of soliton solutions of the Korteweg – de Vries ...
Y. F. Novik
doaj  

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

Contemporary Mathematics, 2020
The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.
Coclite, Giuseppe Maria, di Ruvo, Lorenzo   +1 more
openaire   +2 more sources

On the Korteweg‐de Vries equation: an associated equation [PDF]

International Journal of Mathematics and Mathematical Sciences, 1984
The purpose of this paper is to describe a relationship between the Korteweg‐de Vries (KdV) equation urn:x-wiley:01611712:media:ijmm237357:ijmm237357-math-0001 and another nonlinear partial differential equation of the form urn:x-wiley:01611712:media:ijmm237357:ijmm237357-math-0002 The second equation will be called the Associated Equation (AE ...
Eugene P. Schlereth, Ervin Y. Rodin
openaire   +2 more sources

Boussinesq Solitary-Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy

, 1995
We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg--de Vries hierarchy, we show that the solitary ...
J. C. Montero, J. G. Pereira (a, M. A. Manna, Physique Mathématique Et Théorique, R. A. Kraenkel   +4 more
core   +2 more sources

Exact Solitary Wave Solutions in Nonlinear Carbon Nanotube Composite Beams on Viscoelastic Foundations Under M‐Truncated Derivative

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this study, the nonlinear partial differential equation that governs the free vibration of a carbon nanotube composite beam is analytically investigated using the truncated M‐fractional derivative. This model is a beam supported by a nonlinear viscoelastic base and reinforced by carbon nanotubes.
Nadia Javed, Nauman Ahmed, Muhammad Zafarullah Baber, Tukur Abdulkadir Sulaiman, Taha Radwan, Abeer S. Khalifa, Karim K. Ahmed, Dimitri Mugnai   +7 more
wiley   +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

Nonlocal Mechanical Metamaterials Enabling Soliton Mode Conversion

Small Structures, Volume 6, Issue 12, December 2025.
A mechanical metamaterial (MM) system with nonlocal interactions is presented, where elastic (nontopological) solitons encountering a boundary defect undergo mode conversion and generate backward‐propagating topological solitons. This finding reveals a new mechanism for soliton dynamics in nonlocal systems, offering insights into energy transport, wave
Liang Bai, Ying Li, Yunlong Wang, Jie Sun, Tianzhi Yang   +4 more
wiley   +1 more source

A detailed analysis of the improved modified Korteweg-de Vries equation via the Jacobi elliptic function expansion method and the application of truncated M-fractional derivatives

Results in Physics
Using the Jacobi elliptic function expansion method, which is improved by the novel use of truncated M-fractional derivatives, we thoroughly analyze the improved modified Korteweg-de Vries problem in this paper.
Aamir Farooq, Muhammad Ishfaq Khan, Kottakkaran Sooppy Nisar, Nehad Ali Shah   +3 more
doaj   +1 more source