Results 71 to 80 of about 18,045 (194)

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

Exact traveling wave solutions to higher order nonlinear equations

Journal of Ocean Engineering and Science, 2019
The present paper applies the new generalized (G′/G)-expansion method on three non-linear equations including the fifth-order Korteweg-de Vries equation, (3+1)-dimensional Modified KdV-Zakharov-Kuznetsov equation, and (3+1)-dimensional Jimbo-Miwa ...
Md Nur Alam, Xin Li
doaj   +1 more source

Recognizing Trees From Incomplete Decks

Journal of Graph Theory, Volume 110, Issue 3, Page 322-336, November 2025.
ABSTRACT Given a graph G, the unlabeled subgraphs G − v are called the cards of G. The deck of G is the multiset { G − v : v ∈ V ( G ) }. Wendy Myrvold showed that a disconnected graph and a connected graph both on n vertices have at most ⌊ n 2 ⌋ + 1 cards in common and found (infinite) families of trees and disconnected forests for which this upper ...
Gabriëlle Zwaneveld
wiley   +1 more source

Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation

Mathematics
In this paper, we prove that the isospectral flows associated with both the x-part and the n-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation.
Junwei Cheng, Xiang Tian
doaj   +1 more source

Spectral Parameter Power Series for Zakharov‐Shabat Direct and Inverse Scattering Problems

Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14661-14671, 15 November 2025.
ABSTRACT We study the direct and inverse scattering problems for the Zakharov‐Shabat system. Representations for the Jost solutions are obtained in the form of the power series in terms of a transformed spectral parameter. In terms of that parameter, the Jost solutions are convergent power series in the unit disk.
Vladislav V. Kravchenko
wiley   +1 more source

Cosmology and the Korteweg-de Vries equation [PDF]

Physical Review D, 2012
The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic ...
openaire   +2 more sources

The Generalized Harry Dym Equation

, 2003
The Harry Dym equation is generalized to the system of equations in the manner as the Korteweg - de Vries equation is generalized to the Hirota - Satsuma equation . The Lax and Hamiltonian formulation for this generalization is given.This generalized Lax
Adler, Alber, Antonowicz, Brunelli, Brunelli, Błaszak, Dodd, Gelfand, Hirota, Konopelchenko, Manna, Ziemowit Popowicz   +11 more
core   +1 more source

Learning Physically Interpretable Atmospheric Models From Data With WSINDy

Journal of Geophysical Research: Machine Learning and Computation, Volume 2, Issue 3, September 2025.
Abstract The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data‐driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional ...
Seth Minor, Daniel A. Messenger, Vanja Dukic, David M. Bortz   +3 more
wiley   +1 more source

On the Stochastic Korteweg–de Vries Equation

Journal of Functional Analysis, 1998
The authors study the following stochastic partial differential equation \[ {\partial u\over \partial t}+ {\partial^3 u\over\partial x^3} +u{\partial u\over \partial x} =f+ \Phi(u) {\partial^2 B\over \partial t\partial x}, \tag{*} \] where \(u\) is a random process defined on \((x,t)\in \mathbb{R}\times \mathbb{R}^+\), \(f\) is a deterministic forcing ...
de Bouard, A, Debussche, A
openaire   +2 more sources

The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation [PDF]

, 2014
The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation $\boldsymbol{K} \boldsymbol{M}+\boldsymbol{M} \boldsymbol{K}=\boldsymbol{r}\, \boldsymbol{s}^{T}$
Xu, Dan-dan, Zhang, Da-jun, Zhao, Songling   +2 more
core