Results 71 to 80 of about 8,881 (223)
Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12427-12439, August 2025.ABSTRACT The Ostrovsky equation models long, weakly nonlinear waves, explaining the propagation of surface and internal waves in a rotating fluid. The study focuses on the generalized Ostrovsky equation. Introduced by Levandosky and Liu, this equation demonstrates the existence of solitary waves through variational methods.
Sol Sáez
wiley +1 more source
Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation [PDF]
, 2009 We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV equation in the ...
Ablowitz M +8 more
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Emergence of Coupled Korteweg–de‐Vries Equations in m$m$ Fields
Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT The Korteweg–de‐Vries (KdV) equation is of fundamental importance in a wide range of subjects with generalization to multi‐component systems relevant for multi‐species fluids and cold atomic mixtures. We present a general framework in which a family of multi‐component KdV (mcKdV) equations naturally arises from a broader mathematical structure
Sharath Jose +2 more
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A One-Step Block Hybrid Integrator for Solving Fifth Order Korteweg-de Vries Equations
Journal of Nigerian Society of Physical Sciences, 2022 Fifth-order Korteweg-de Vries (KdV) equations, arise in modeling waves phenomena such as the propagation of shallow water waves over a flat surface, gravity-capillary waves and sound waves in plasmas.
Olumide O. Olaiya +2 more
doaj +1 more source
On a Schwarzian PDE associated with the KdV Hierarchy [PDF]
, 1999 We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy.
Ablowitz +18 more
core +2 more sources
Finite‐Dimensional Reductions and Finite‐Gap‐Type Solutions of Multicomponent Integrable PDEs
Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well‐known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup ...
Alexey V. Bolsinov +2 more
wiley +1 more source
Electronic Journal of Differential Equations, 2003 We present a new method for studying the interaction of solitons for non-integrable Korteweg-de Vries (KdV) type equations with small dispersion and test this method for the KdV equation.
Vladimir G. Danilov +1 more
doaj
A Note on the Fractional Generalized Higher Order KdV Equation
Journal of Function Spaces, 2018 We obtain exact solutions to the fractional generalized higher order Korteweg-de Vries (KdV) equation using the complex method. It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations ...
Yongyi Gu
doaj +1 more source
Andrew Lenard: A Mystery Unraveled [PDF]
, 2005 The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the "Lenard recursion formula". The story about the discovery of the formula told by Andrew Lenard is the subject of this article.Comment: Published in SIGMA (Symmetry,
Praught, Jeffery, Smirnov, Roman G.
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Nonlinear inference capacity of fiber‐optical extreme learning machines
Nanophotonics, Volume 14, Issue 16, Page 2749-2760, August 2025.Abstract The intrinsic complexity of nonlinear optical phenomena offers a fundamentally new resource to analog brain‐inspired computing, with the potential to address the pressing energy requirements of artificial intelligence. We introduce and investigate the concept of nonlinear inference capacity in optical neuromorphic computing in highly nonlinear
Sobhi Saeed +5 more
wiley +1 more source