Results 101 to 110 of about 8,881 (223)

Physical vs mathematical origin of the extended KdV and mKdV equations

AIMS Mathematics
The higher-order Korteweg-de Vries (KdV) and modified KdV (mKdV) equations are derived from a physical model describing a three-component plasma composed of cold fluid ions and two species of Boltzmann electrons at different temperatures.
Saleh Baqer, Theodoros P. Horikis, Dimitrios J. Frantzeskakis   +2 more
doaj   +1 more source

Nonlinear Modes of Liquid Drops as Solitary Waves

, 2000
The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves.
A. Ludu, A. Ludu, A. Ludu, E. H. Trinh, E. H. Trinh, E. Trinh, F. H. Busse, G. L. Lamb, H.-L. Lu, J. A. Tsamopoulos, J. P. Draayer, P. Annamalai, P. L. Marston, P. Rosenau, R. E. Apfel, R. G. Holt, R. H. Durisen, R. Natarajan, R. Natarajan, S. Dramanyan, T. Shi, Y. G. Kevrekidis, Y. Tian   +22 more
core   +1 more source

Numerical Solution of the Rosenau‐KdV‐RLW equation via combination of a polynomial scaling function collocation and finite difference method

Mathematical Methods in the Applied Sciences, Volume 48, Issue 3, Page 4015-4034, February 2025.
In this paper, we established a polynomial scaling method to investigate the numerical solution of Rosenau–Korteweg De Vries‐regularized long wave (Rosenau‐KdV‐RLW) equation. We start with discretization of the time variable of the equation using a finite difference approach equipped with a linearization.
Ömer Oruç, Alaattin Esen, Fatih Bulut
wiley   +1 more source

KdV-type equations linked via Baecklund transformations: remarks and perspectives

, 2018
Third order nonlinear evolution equations, that is the Korteweg-deVries (KdV), modified Korteweg-deVries (mKdV) equation and other ones are considered: they all are connected via Baecklund transformations.
Carillo, Sandra
core   +1 more source

Observations of Mode‐One Nonlinear Internal Waves (NLIW) of Opposite Polarity in Changing Background Conditions

Journal of Geophysical Research: Oceans, Volume 130, Issue 2, February 2025.
Abstract The transformation of internal waves on continental shelves is important to mass transfer, nutrient replenishment, and heat transfer. Yet, the transfer of energy from larger to smaller scale or between nonlinear internal waves (NLIW) themselves remains poorly understood.
A. Moncuquet, N. L. Jones, A. P. Zulberti, L. Bordois, F. Dufois, P. Lazure   +5 more
wiley   +1 more source

Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method

Journal of Applied Mathematics, 2012
The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series ...
Mojtaba Nazari, Faisal Salah, Zainal Abdul Aziz, Merbakhsh Nilashi   +3 more
doaj   +1 more source

Shock Waves in Nonlinear Transmission Lines

physica status solidi (b), Volume 262, Issue 1, January 2025.
Interaction between the small amplitude travelling waves (“the sound”) and the shock waves in the transmission line containing both nonlinear capacitors and nonlinear inductors is considered. The profiles of the shocks and of the kinks are studied. The latter profiles are expressed in terms of elementary functions.
Eugene Kogan
wiley   +1 more source

Traveling wave solution of (3+1)-dimensional negative-order KdV-Calogero-Bogoyavlenskii-Schiff equation

AIMS Mathematics
We explored the (3+1)-dimensional negative-order Korteweg-de Vries-alogero-Bogoyavlenskii-Schiff (KdV-CBS) equation, which develops the classical Korteweg-de Vries (KdV) equation and extends the contents of nonlinear partial differential equations.
Musong Gu, Chen Peng, Zhao Li
doaj   +1 more source

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   +1 more source

Shallow water cnoidal wave interactions [PDF]

Nonlinear Processes in Geophysics, 1994
The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV) and Kadomtsev-Petvishvilli (KP) equations, are considered.
A. R. Osborne
doaj