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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[...]
