88 citations · 103 across the 11 of their papers we have counts for
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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 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…
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…
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…