Results 71 to 80 of about 8,283 (176)

Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials

, 2009
A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative Lagrangian ...
Abraham R, Boyko V M, Boyko V M, Briskin M, Cariñena J F, Crampin M, Crampin M, Damianou P A, Darboux G, Darboux G, Darboux G, Davis H T, Erbe L, Fernandes R L, Francoise J P, Grundland A M, José F Cariñena, Lopuszanski J, López C, Manuel F Rañada, Murphy G M, Nucci M C, Partha Guha, Polyanin A D, Sarlet W, Sarlet W, Zwillinger D   +26 more
core   +1 more source

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

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

The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

, 2005
We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure.
Aoyama H, Crum M M, Gesztesy F, Khare A, Ronveaux A, Smirnov A O, Takemura K, Takemura K, Takemura K, Takemura K, Treibich A, Treibich A, Whittaker E T   +12 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

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

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

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

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