Results 71 to 80 of about 8,902 (211)

On the deep‐water and shallow‐water limits of the intermediate long wave equation from a statistical viewpoint

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley   +1 more source

Explicit solutions to the Korteweg-de Vries equation on the half line [PDF]

, 2006
Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection ...
Ablowitz M J, Ablowitz M J, Aktosun T, Aktosun T, Bart H, Carl B, Chadan K, Coddington E A, Cornelis van der Mee, Deift P, Faddeev L D, Hirota R, Huang N N, Konopel'chenko B G, Marchenko V A, Marchenko V A, Matveev V B, Treibich A, Tuncay Aktosun   +18 more
core   +2 more sources

Analysis of the Generalized Ostrovsky Equation in the Propagation of Surface and Internal Waves in Rotating Fluids

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

White-Noise-Driven KdV-Type Boussinesq System

Mathematics
The white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize features from both the ...
Aissa Boukarou, Safa M. Mirgani, Khaled Zennir, Keltoum Bouhali, Sultan S. Alodhaibi   +4 more
doaj   +1 more source

Abelian versus non-Abelian Baecklund Charts: some remarks [PDF]

, 2018
Connections via Baecklund transformations among different non-linear evolution equations are investigated aiming to compare corresponding Abelian and non Abelian results. Specifically, links, via Baecklund transformations, connecting Burgers and KdV-type
Carillo, Sandra, Schiavo, Mauro Lo, Schiebold, Cornelia   +2 more
core   +2 more sources

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, Manas Kulkarni, Vishal Vasan   +2 more
wiley   +1 more source

Parameter Estimation for Stochastic Korteweg–de Vries Equations

Axioms
In this paper, we propose two methods for parameter estimation in stochastic Korteweg–de Vries (KdV) equations with unknown parameters. Both methods are based on the numerical discretization of the stochastic KdV equation. Moreover, we further propose an
Zhenyu Lang, Xiuling Yin, Yanqin Liu, Yaru Wang   +3 more
doaj   +1 more source

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, Andrey Yu. Konyaev, Vladimir S. Matveev   +2 more
wiley   +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

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, Mehmet Müftüoğlu, Glitta R. Cheeran, Thomas Bocklitz, Bennet Fischer, Mario Chemnitz   +5 more
wiley   +1 more source