Results 71 to 80 of about 8,235 (175)

Product of Exponentials (POE) Splines on Lie‐Groups: Limitations, Extensions, and Application to SO(3)$$ SO(3) $$ and SE(3)$$ SE(3) $$

International Journal for Numerical Methods in Engineering, Volume 126, Issue 14, 30 July 2025.
ABSTRACT Existing methods for constructing splines and Bézier curves on a Lie group G$$ G $$ involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of G$$ G $$.
Andreas Müller
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  

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

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations

, 2010
Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials.
Agarwal R P, Caputo M, Craiem D, Diethelm K Weibeer M Le Mehaute A Machado J A Trigeasson J C Sabatier J, Dzherbashyan M M, Feder J, Humbert P, Humbert P, Kilbas A A, Mainardi F, Mittag-Leffler G, Momani S, Oldham K B, Podlubny I, Podlubny I, Spiegel M R, Tihonov A N, Trifce Sandev, Yuste S B, Živorad Tomovski   +19 more
core   +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

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

Singular Isotonic Oscillator, Supersymmetry and Superintegrability

Symmetry, Integrability and Geometry: Methods and Applications, 2012
In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner H_a, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations.
Ian Marquette
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

Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices

Symmetry, Integrability and Geometry: Methods and Applications, 2006
We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices.
Hjalmar Rosengren
doaj  

Old and New Reductions of Dispersionless Toda Hierarchy

Symmetry, Integrability and Geometry: Methods and Applications, 2012
This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of ''Landau-Ginzburg potentials'' that play the role of reduced Lax functions ...
Kanehisa Takasaki
doaj   +1 more source