Results 81 to 90 of about 8,235 (175)

Simple Darboux points of polynomial planar vector fields

Journal of Pure and Applied Algebra, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Numerical Approaches in Nonlinear Fourier Transform‐Based Signal Processing for Telecommunications

Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.
ABSTRACT We discuss applications of the inverse scattering transform, also known as the nonlinear Fourier transform (NFT) in telecommunications, both for nonlinear optical fiber communication channel equalization and time‐domain signal processing techniques.
Egor Sedov, Igor Chekhovskoy, Mikhail Fedoruk, Sergey Turitsyn   +3 more
wiley   +1 more source

Action of derivations on polynomials and on Jacobian derivations

Researches in Mathematics
Let $\mathbb K$ be a field of characteristic zero, $A := \mathbb K[x_{1}, x_{2}]$ the polynomial ring and $W_2(\mathbb K)$ the Lie algebra of all $\mathbb K$-derivations on $A$. Every polynomial $f \in A$ defines a Jacobian derivation $D_f\in W_2(\mathbb
O.Ya. Kozachok, A.P. Petravchuk
doaj   +1 more source

Convergence and nonconvergence in a nonlocal gradient flow

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract We study the asymptotic convergence as t→∞$t\rightarrow \infty$ of solutions of ∂tu=−f(u)+∫f(u)$\partial _t u=-f(u)+\int f(u)$, a nonlocal differential equation that is formally a gradient flow in a constant‐mass subspace of L2$L^2$ arising from simplified models of phase transitions. In case the solution takes finitely many values, we provide
Sangmin Park, Robert L. Pego
wiley   +1 more source

Advanced Mathematical Approaches for the Kadomtsev–Petviashvili and Bogoyavlensky–Konopelchenko Equations in Applied Sciences

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
The Kadomtsev–Petviashvili (KP) equation and the Bogoyavlensky–Konopelchenko (BK) equation are fundamental models in the study of nonlinear wave dynamics, describing the evolution of weakly dispersive, quasi‐two‐dimensional (2D) wave phenomena in integrable systems.
Md. Abdul Aziz, Jingli Ren
wiley   +1 more source

Stationary‐Angle Conditions and Bertrand Offsets in Timelike‐Ruled Surfaces

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this study, we introduce the concept of stationary‐angle timelike‐ruled surfaces and examine their geometric properties, particularly in relation to their Bertrand offsets. A timelike‐ruled surface is generated by the motion of a straight ruling along a striction curve, and its structure is analyzed using the Blaschke and Darboux frames.
Areej A. Almoneef, Rashad A. Abdel-Baky, Leopoldo Greco   +2 more
wiley   +1 more source

Algebraic construction of the Darboux matrix revisited

, 2009
We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case.
Arnold W I, Bart H, Belinsky V A, Bobenko A I, Bobenko A I, Bohner M, Boiti M, Boutet de Monvel A, Burtsev S P, Cieśliński J, Cieśliński J L, Cieśliński J L, Cieśliński J L, Cieśliński J L, Coley A, Darboux G, Doktorov E V, Gohberg I, Gu G C, Gu G C, Guest M A, Hoenselaers C, Its A R, Jan L Cieśliński, Krichever I M, Leble S B, Levi D, Matveev V B, Mañas M, Meinel R, Mikhailov A V, Mikhailov A V, Neugebauer G, Nijhoff F, Nimmo J J C, Novikov S P, Oevel W, Pressley A N, Rogers C, Sakhnovich A L, Sakhnovich L A, Sakhnovich L A, Saleem U, Shabat A B, Shin H J, Terng C L, Uhlenbeck K, Zakharov V E, Zakharov V E, Zakharov V E, Zhou Z X   +50 more
core   +2 more sources

Fields of rational constants of cyclic factorizable derivations

Electronic Journal of Differential Equations, 2015
We describe all rational constants of a large family of four-variable cyclic factorizable derivations. Thus, we determine all rational first integrals of their corresponding systems of differential equations.
Janusz Zielinski
doaj  

On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials

Journal of Mathematical Analysis and Applications, 2014
We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal ...
Carlos Álvarez-Fernández, Manuel Mañas   +1 more
openaire   +3 more sources

Darboux transforms on Band Matrices, Weights and associated Polynomials

, 2000
Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In "Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems", Comm. Math. Phys. 207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights lead to "moments", polynomials defined by determinants of matrices ...
Adler, Mark, van Moerbeke, Pierre
openaire   +3 more sources