Results 51 to 60 of about 187 (156)

Improved Gevrey‐1 Estimates of Formal Series Expansions of Center Manifolds

Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.
ABSTRACT In this paper, we show that the coefficients ϕn$\phi _n$ of the formal series expansions ∑n=1∞ϕnxn∈xC[[x]]$\sum _{n=1}^\infty \phi _n x^n\in x\mathbb {C}[[x]]$ of center manifolds of planar analytic saddle‐nodes grow like Γ(n+a)$\Gamma (n+a)$ (after rescaling x$x$) as n→∞$n\rightarrow \infty$.
Kristian Uldall Kristiansen
wiley   +1 more source

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.
This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
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

Orthogonal Laurent Polynomials of Two Real Variables

Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.
ABSTRACT In this paper, we consider an appropriate ordering of the Laurent monomials xiyj$x^{i}y^{j}$, i,j∈Z$i,j \in \mathbb {Z}$ that allows us to study sequences of orthogonal Laurent polynomials of the real variables x$x$ and y$y$ with respect to a positive Borel measure μ$\mu$ defined on R2$\mathbb {R}^2$ such that ({x=0}∪{y=0})∩supp(μ)=∅$(\lbrace ...
Ruymán Cruz‐Barroso, Lidia Fernández
wiley   +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

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  

First and Second Integrals of Hopf–Langford-Type Systems

Axioms
The work examines a seven-parameter, three-dimensional, autonomous, cubic nonlinear differential system. This system extends and generalizes the previously studied quadratic nonlinear Hopf–Langford-type systems.
Vassil M. Vassilev, Svetoslav G. Nikolov
doaj   +1 more source

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

Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems

Symmetry, Integrability and Geometry: Methods and Applications, 2012
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (
Hiroshi Miki, Hiroaki Goda, Satoshi Tsujimoto   +2 more
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