Results 101 to 110 of about 22,064 (260)

the Solving Partial Differential Equations by using Efficient Hybrid Transform Iterative Method

Tikrit Journal of Pure Science
The aim of this article is to propose an efficient hybrid transform iteration method that combines the homotopy perturbation approach, the variational iteration method, and the Aboodh transform forsolving various partial differential equations.
Ruaa Shawqi Ismael, Ali Al -Fayadh, Saad M. Salman   +2 more
doaj   +1 more source

Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations

Demonstratio Mathematica, 2021
The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian ...
Appadu Appanah Rao, Kelil Abey Sherif
doaj   +1 more source

Superposition solutions to the extended KdV equation for water surface waves

, 2017
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects.
Infeld, Eryk, Karczewska, Anna, Rozmej, Piotr   +2 more
core   +1 more source

Quasilinear Differential Constraints for Parabolic Systems of Jordan‐Block Type

Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.
ABSTRACT We prove that linear degeneracy is a necessary conditions for systems in Jordan‐block form to admit a compatible quasilinear differential constraint. Such condition is also sufficient for 2×2$2\times 2$ systems and turns out to be equivalent to the Hamiltonian property.
Alessandra Rizzo, Pierandrea Vergallo
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

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

The conservative Camassa–Holm flow with step‐like irregular initial data

Proceedings of the London Mathematical Society, Volume 130, Issue 5, May 2025.
Abstract We extend the inverse spectral transform for the conservative Camassa–Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boundedness‐type conditions at the other endpoint. The latter condition appears to be close to optimal in a certain sense for the well‐posedness of the conservative ...
Jonathan Eckhardt, Aleksey Kostenko
wiley   +1 more source

Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations

, 2000
Weakly damped forced KdV equation provides a dissipative semigroup on $L_x^2$. We prove that this semigroup enjoys an asymptotic smoothing effect, i.e. that all solutions converge towards a set of smoother solutions, when time goes to infinity.
O. Goubet
semanticscholar   +1 more source

Foundations of Ghost Stability

Fortschritte der Physik, Volume 73, Issue 4, April 2025.
Abstract The authors present a new method to analytically prove global stability in ghost‐ridden dynamical systems. The proposal encompasses all prior results and consequentially extends them. In particular, it is shown that stability can follow from a conserved quantity that is unbounded from below, contrary to expectation.
Verónica Errasti Díez, Jordi Gaset Rifà, Georgina Staudt   +2 more
wiley   +1 more source

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.
This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
wiley   +1 more source