Elena Medina

TL;DR: In this paper, it was shown that the profile of any such solution consists of an imploding, smoothed-out shock wave that collapses into a Dirac mass when the singularity is formed, and the differences between this type of behaviour and that known to occur for blowing-up solutions of (S) in the case N = 2 are discussed.

TL;DR: In this paper, it was shown that when the space dimension N is equal to three, (S) has radial solutions with finite mass that blow-up in finite time in a self-similar manner.

TL;DR: In this article, a general scheme for analyzing reductions of dispersionless integrable hierarchies is presented based on a method for determining the S-function by means of a system of first-order differential equations.

TL;DR: In this article, a family of solutions of the KP hierarchy obtained by Sato is analyzed for the KP equation and it is found that these solutions describe processes of interaction of an arbitrary number of resonant solitons.

TL;DR: In this article, it was shown that the quantum field theoretical formulation of the -function theory has a geometrical interpretation within the classical transformation theory of conjugate nets, and that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinearly identity for multidimensional quadrilateral lattice equations.