Spectral Curves for Third-Order ODOs

Autor: Sonia L. Rueda, Maria-Angeles Zurro

Publikováno v: Axioms, Vol 13, Iss 4, p 274 (2024)

Spectral curves are algebraic curves associated to commutative subalgebras of rings of ordinary differential operators (ODOs). Their origin is linked to the Korteweg–de Vries equation and to seminal works on commuting ODOs by I. Schur and Burchnall

Externí odkaz: https://doaj.org/article/18d40c54118f4b0087fd798af68bac5f

Semialgebraic sets and real binary forms decompositions

Autor: Maria-Angeles Zurro, Macarena Ansola, A. Díaz-Cano

Publikováno v: Biblos-e Archivo. Repositorio Institucional de la UAM
instname
E-Prints Complutense: Archivo Institucional de la UCM
Universidad Complutense de Madrid
E-Prints Complutense. Archivo Institucional de la UCM

The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d-th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real bi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7cc14148e2b05e476c3a2941a23fa895
https://eprints.ucm.es/id/eprint/65061/

Commuting Ordinary Differential Operators and the Dixmier Test

Autor: Sonia L. Rueda, Maria-Angeles Zurro, Emma Previato

The Burchnall-Chaundy problem is classical in differential algebra, seeking to describe all commutative subalgebras of a ring of ordinary differential operators whose coefficients are functions in a given class. It received less attention when posed

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d46a2e4b084de91cf806f0601e54650c

Rational KdV Potentials and Differential Galois Theory

Autor: Juan J. Morales-Ruiz, Maria-Angeles Zurro, Sonia Jim Énez, Raquel Sánchez-Cauce

Publikováno v: Biblos-e Archivo. Repositorio Institucional de la UAM
instname
Biblos-e Archivo: Repositorio Institucional de la UAM
Universidad Autónoma de Madrid

In this work, using differential Galois theory, we study the spectral problem of the one-dimensional Schr\"odinger equation for rational time dependent KdV potentials. In particular, we compute the fundamental matrices of the linear systems associate

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::913d2e45fd86d52ec9ab0387dd010cfa

On the rings of formal solutions of polynomial differential equations

Autor: Maria-Angeles Zurro

Publikováno v: Banach Center Publications. 44:277-292

Introduction. The Gevrey series appeared as formal solutions of partial differential equations of second order ([G]). In 1903 Maillet ([Mi]) proved that the formal solutions of ordinary differential equations with polynomial coefficients are of this

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::df58d1589de6178a1f37d86a1c728f76
https://doi.org/10.4064/-44-1-277-292