Información del autor
Autor Mañas Baena, Manuel |
Documentos disponibles escritos por este autor (42)
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The dispersionless KP hierarchy is considered from the point of view of the twistor formalism. A set of explicit additional symmetries is characterized and its action on the solutions of the twistor equations is studied. A method for dealing wit[...]texto impreso
In this paper the Galilean, scaling and translational self-similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite-dimensional Grassmannian. The string equations of the one-matrix model correspond to the [...]texto impreso
We consider the sequences of matrix bi-orthogonal polynomials with respect to the bilinear forms ((R) over cap) and ((L) over cap)texto impreso
Darboux transformation is reconsidered for the supersymmetric KdV system. By iterating the Darboux transformation, a supersymmetric extension of the Crum transformation is obtained for the Manin-Radul SKdV equation, in doing so one gets Wronskia[...]texto impreso
In this paper we present a vectorial Darboux transformation, in terms of ordinary determinants, for the supersymmetric extension of the Korteweg-de Vries equation proposed by Manin and Radul. It is shown how this transformation reduces to the Ko[...]texto impreso
We construct Darboux transformations for the super-symmetric KP hierarchies of Manin-Radul and Jacobian types. We also consider the binary Darboux transformation for the hierarchies. The iterations of both type of Darboux transformations are bri[...]texto impreso
Sequences of discrete Levy and adjoint Levy transformations for multidimensional quadrilateral lattices are studied. After a suitable number of iterations we show how all the relevant geometrical features of the transformed quadrilateral lattice[...]texto impreso
Mañas Baena, Manuel ; Martínez Alonso, Luis | Departamento de Física Teórica II (Métodos Matemáticos de la Física) | 2015En este manual se revisan diferentes aspectos sobre las ecuaciones diferenciales en derivadas parciales de utilidad para los físicos. Se elaboraron como notas de clase de la asignatura Ecuaciones II, del plan 1993 de la Licenciatura de Física de[...]texto impreso
Valle Granda, Javier del ; Gómez Nicola, Ángel ; González Herrera, Elvira María ; Mañas Baena, Manuel ; Coronado, E. ; Vicent López, José Luis | American Physical Society | 2017-06-12Superconducting 2H-NbSe_2 single crystals show intrinsic low pinning values. Therefore, they are ideal materials with which to explore fundamental properties of vortices. (V, I) characteristics are the experimental data we have used to investiga[...]texto impreso
Inspired by the results of Jonas, Einsenhart, Demoulin, and Bianchi on the permutability property of classical geometrical transformations of conjugate nets and its reductions-of pseudo-orthogonal, pseudo-symmetric, and pseudo-Egorov types-dress[...]texto impreso
We show how Ramond free neutral Fermi fields lead to a ?-function theory of BKP type which describes iso-orthogonal deformations of systems of orthogonal curvilinear coordinates. We also provide a vertex operator representation for the classical[...]texto impreso
The bilinear equations of the N-component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and orthogonal nets, respectively. The main geometrical obj[...]texto impreso
An alternative expression for the Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type is derived from the LU factorization of the moment matrix of a given measure and two sets of weights. We use the action of the genera[...]texto impreso
Branquinho, Amilcar ; Foulquié Moreno, Ana ; Mañas Baena, Manuel | Academic Press Inc Elsevier Science | 2021-02-15In this paper we use the Riemann-Hilbert problem, with jumps supported on appropriate curves in the complex plane, for matrix biorthogonal polynomials and apply it to find Sylvester systems of differential equations for the orthogonal polynomial[...]texto impreso
Ariznabarreta, Gerardo ; García Ardila, Juan ; Mañas Baena, Manuel ; Marcellan, Francisco | World Scientific Publishing Co Pte Ltd | 2019-08In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line are studied. The orthogonality is understood in a broad sense, and is given in terms of a nondegenerate continuous sesquilinear form, which in turn is de[...]texto impreso
Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss–Borel factorization of two, left and a right, Cantero–Morales–Velázquez block moment matrices, which are constr[...]texto impreso
Multiple orthogonality is considered in the realm of a Gauss-Borel factorization problem for a semi-infinite moment matrix. Perfect combinations of weights and a finite Borel measure are constructed in terms of M-Nikishin systems. These perfect [...]texto impreso
Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associa[...]texto impreso
We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomialstexto impreso
For a family of Poisson algebras, parametrized by r is an element of Z, and an associated Lie algebraic splitting, we consider the factorization of given canonical transformations. In this context, we rederive the recently found rth dispersionle[...]texto impreso
A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations[...]texto impreso
Guil Guerrero, Francisco ; Mañas Baena, Manuel ; Martínez Alonso, Luis | IOP Publishing | 2003-06-13The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for[...]texto impreso
We connect the theory of orthogonal Laurent polynomials on the unit circle and the theory of Toda-like integrable systems using the Gauss-Borel factorization of a Cantero-Moral-Velazquez moment matrix, that we construct in terms of a complex qua[...]texto impreso
We reduce the vectorial binary Darboux transformation for the Manin-Radul supersymmetric KdV system in such a way that it preserves the Manin-Radul-Mathieu supersymmetric KdV equation reduction. Expressions in terms of bosonic Pfaffians are prov[...]texto impreso
Los sistemas integrables son de extremo interes en Fisica y Matematicas. Ello se debe a las asombrosas propiedades que presentan desde ambos puntos de vista. En este trabajo se analizan ciertas propiedades geometricas de tales sistemas. Los prob[...]texto impreso
n this paper, matrix orthogonal polynomials in the real line are described in terms of a RiemannHilbert problem. This approach provides an easy derivation of discrete equations for the corresponding matrix recursion coefficients. The discrete eq[...]texto impreso
We introduce an S-function formulation for the recently found rth dispersionless modified KP and rth dispersionless Dym hierarchies, giving also a connection of these S-functions with the Orlov functions of the hierarchies. Then, we discuss a re[...]texto impreso
The string equation appearing in the double scaling limit of the Hermitian one–matrix model, which corresponds to a Galilean self–similar condition for the KdV hierarchy, is reformulated as a scaling self–similar condition for the Ur–KdV hierarc[...]texto impreso
Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formu[...]texto impreso
Cassatella-Contra, Giovanni A ; Mañas Baena, Manuel ; Tempesta, Piergiulio | IOP publishing ltd | 2014-09We study the analytic properties of a matrix discrete system introduced by Cassatella and Manas (2012 Stud. Appl. Math. 128 252-74). The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters [...]texto impreso
The periodic flag manifold (in the Sato Grassmannian context) description of the modified Korteweg-de Vries hierarchy is used to analyse the translational and scaling self-similar solutions of this hierarchy. These solutions are characterized by[...]texto impreso
Martínez Alonso, Luis ; Medina Reus, Elena ; Mañas Baena, Manuel | American Institute of Physics | 2006-08A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The ?-functions of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characte[...]texto impreso
Martínez Alonso, Luis ; Medina Reus, Elena ; Mañas Baena, Manuel | American Institute of Physics | 2006-08A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The tau-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are charact[...]texto impreso
The exponential solutions of the Darboux equations for conjugate nets is considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the Darboux system, whic[...]texto impreso
The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated with an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov-Shabat equations are characterized. [...]texto impreso
The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov-Schulman operators is introd[...]texto impreso
We consider the relation of the multicomponent 2D Toda hierarchy with the matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresponding generalized matrix orthogonal polyn[...]texto impreso
Based on the eigenfunction symmetry constraint of the q-deformed modified KP hierarchy, a q-deformed mKP hierarchy with self-consistent sources (q-mKPHSCSs) is constructed. The q-mKPHSCSs contain two types of q-deformed mKP equation with self-co[...]texto impreso
Guil Guerrero, Francisco ; Mañas Baena, Manuel ; Martínez Alonso, Luis | IOP Publishing | 2003-04-11A general scheme for analysing reductions of Whitham hierarchies is presented. It is based on a method for determining the S-function by means of a system of first-order partial differential equations. Compatibility systems of differential equat[...]texto impreso
Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:Z(N)--> R-M, N less tha[...]texto impreso
We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian type de[...]texto impreso
The vectorial extension of the Ribaucour transformation for the Lame equations bf orthogonal conjugate nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data[...]