Results 81 to 90 of about 8,283 (176)

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

Stability of Standing Periodic Waves in the Massive Thirring Model

Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.
ABSTRACT We analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability of the standing periodic waves can be studied by using their Lax spectrum.
Shikun Cui, Dmitry E. Pelinovsky
wiley   +1 more source

Detecting and determining preserved measures and integrals of rational maps

, 2020
In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use of symbolic algebra tools.
Celledoni, Elena, Evripidou, Charalambos, McLaren, David, Owren, Brynjulf, Quispel, Reinout, Tapley, Benjamin   +5 more
core  

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

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

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

Galoisian Approach to integrability of Schr\"odinger Equation [PDF]

, 2010
In this paper, we examine the non-relativistic stationary Schr\"odinger equation from a differential Galois-theoretic perspective. The main algorithmic tools are pullbacks of second order ordinary linear differential operators, so as to achieve rational ...
Dedicated To Jerry Kovacic, In Memoriam, Jacques-arthur Weil, Juan J. Morales-ruiz, Primitivo B. Acosta-humánez   +4 more
core  

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

Spectral analysis for the exceptional Xm-Jacobi equation

Electronic Journal of Differential Equations, 2015
We provide the mathematical foundation for the $X_m$-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional $X_m$-Jacobi orthogonal polynomials as eigenfunctions.
Constanze Liaw, Lance Littlejohn, Jessica Stewart Kelly   +2 more
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