Results 71 to 80 of about 6,848 (171)

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

Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains

, 2002
A chain of one-dimensional Schr\"odinger operators connected by successive Darboux transformations is called the ``Darboux chain'' or ``dressing chain''. The periodic dressing chain with period $N$ has a control parameter $\alpha$.
Adams, Adler, Burchnall, Drinfeld, Dubrovin, Dubrovin, Flaschka, Garnier, Harnad, Harnad, Kanehisa Takasaki, Krichever, Lax, McKean, Moore, Noumi, Novikov, Okamoto, Shabat, Shabat, Sklyanin, Veselov   +21 more
core   +4 more sources

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

Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom

, 2009
We consider natural complex Hamiltonian systems with $n$ degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of degree $k>2$.
A. Guillot, A. J. Maciejewski, A. J. Maciejewski, A. K. Tsikh, A. Koz’owski, D. Cox, D. Cox, G. Biernat, G. Biernat, G. Biernat, H. A. Schwarz, H. Yoshida, H. Yoshida, I.A. Aĭzenberg, I.R. Shafarevich, J. Hietarinta, J. Hietarinta, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, K. Nakagawa, M. Audin, M. Przybylska, M. Przybylska, M.A. Almeida, P. Griffiths, P.A. Griffiths, P.F. Baum, S. L. Ziglin, S. L. Ziglin, T. Kimura   +33 more
core   +2 more sources

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

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

Whittaker-Hill equation and semifinite-gap Schroedinger operators

, 2009
A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux ...
A. D. Hemery, A. P. Veselov, Darboux G., Erdélyi A., Kato T., Levitan B. M., Liapounoff A., Magnus W., Reed M., Ushveridze A. G., Whittaker E. T.   +10 more
core   +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

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