88 citations · 103 across the 11 of their papers we have counts for
11 papers
From Spectral Curves to Variational Equations: Geometry and Differential Galois Theory of KdV Cnoidal Waves
Juan Jose Morales-Ruiz, Jean Pierre Ramis, Maria-Angeles Zurro
We provide a spectral geometric description of the KdV variational equation around cnoidal waves in terms of two interacting spectral curves.
Computing almost commuting bases of ODOs and Gelfand-Dickey hierarchies
Antonio Jiménez-Pastor, Sonia L. Rueda, Maria-Angeles Zurro +2
Almost commuting operators were introduced in 1985 by George Wilson to present generalizations of the Korteweg-de Vries hierarchy, nowadays known as Gelfand-Dickey (GD) hierarchies…
Computing defining ideals of space spectral curves for algebro-geometric third order ODOs
Sonia L. Rueda, Maria-Angeles Zurro
Commuting pairs of ordinary differential operators (ODOs) have been related to plane algebraic curves since the work of Burchnall and Chaundy a century ago. We introduce now the co…
Burchnall-Chaundy polynomials for matrix ODOs and Picard-Vessiot Theory
Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro
Burchnall and Chaundy showed that if two ODOs , with analytic coefficients commute there exists a polynomial with complex coefficients such that , called…
Factoring Third Order Ordinary Differential Operators over Spectral Curves
Sonia L. Rueda, Maria-Angeles Zurro
We consider the classical factorization problem of a third order ordinary differential operator , for a spectral parameter . It is assumed that is an algebro-geometric…
On real Waring decompositions of real binary forms
Macarena Ansola, Antonio Díaz-Cano, M. Angeles Zurro
The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial of degree as a finite sum of -{th} powers of linear forms. In this work we give a…
Factorization of KdV Schrödinger operators using differential subresultants
Juan J. Morales-Ruiz, Sonia L. Rueda, Maria-Angeles Zurro
We address the classical factorization problem of a one dimensional Schrödinger operator , for a stationary potential of the KdV hierarchy but, in this occasio…
Commuting Ordinary Differential Operators and the Dixmier Test
Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro
The Burchnall-Chaundy problem is classical in differential algebra, seeking to describe all commutative subalgebras of a ring of ordinary differential operators whose coefficients…
The Outer Stellar Halos of Galaxies: how Radial Merger Mass Deposition, Shells and Streams depend on Infall-Orbit Configurations
Geray S. Karademir, Rhea-Silvia Remus, Andreas Burkert +5
Galaxy mergers are a fundamental part of galaxy evolution. To study the resulting mass distributions of different kinds of galaxy mergers, we present a simulation suite of 36 high-…
Spectral Picard-Vessiot fields for Algebro-geometric Schrödinger operators
Juan J. Morales-Ruiz, Sonia L. Rueda, Maria-Angeles Zurro
This work is a galoisian study of the spectral problem , for algebro-geometric second order differential operators , with coefficients in a differential field, whose fiel…
Semialgebraic decomposition of real binary forms of a given degree's space
Macarena Ansola, Antonio Díaz-Cano, M. Angeles Zurro
The Waring Problem over polynomial rings asks for how to decompose an homogeneous polynomial of degree as a finite sum of powers of linear forms. First, we give a cons…