Related papers: The generalized KP hierarchy
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and…
We construct the matrix generalization of the N=2 supersymmetric GNLS hierarchies. This is done by exhibiting the corresponding matrix super Lax operators in terms of N=2 superfields in two different superfield bases. We present the second…
The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the…
Unifying hierarchies of integrable equations are discussed. They are constructed via generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical…
The multisymplectic structure of the KP equation is obtained directly from the variational principal. Using the covariant De Donder-Weyl Hamilton function theories, we reformulate the KP equation to the multisymplectic form which proposed…
We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and…
We construct the bi-Hamiltonian structure of the waterbag model of dKP and establish the third-order Hamiltonian operator associated with the waterbag model. Also, the symmetries and conserved densities of rational type are discussed.
Exploiting the residual gauge freedom in the formulation of constrained KP hierarchy a number of new integrable systems are derived including hierarchies of Kundu-Eckhaus equation and higher order nonlinear extensions of Yajima-Oikawa and…
In this paper we give a geometric description in terms of the Grassmann manifold of Segal and Wilson, of the reduction of the KP hierarchy known as the vector $k$-constrained KP hierarchy. We also show in a geometric way that these…
We investigate the bi-Hamiltonian structure of the waterbag model of dKP for two component case. One can establish the third-order and first-order Hamiltonian operator associated with the waterbag model. Also, the dispersive corrections are…
We generalize Toda--like integrable lattice systems to non--symmetric case. We show that they possess the bi--Hamiltonian structure.
Generalizing a construction of P. Vanhaecke, we introduce a large class of degenerate (i.e., associated to a degenerate Poisson bracket) completely integrable systems on (a dense subset of) the space $\R^{2d+n+1}$, called the generalized…
We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a…
We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in which the space coordinate is identified with an…
We exhibit the dispersionless limit of the extended discrete KP hierarchy.
A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami-Kanno super KdV hierarchy and constrained modified super KP hierarchy are…
We study a Kadomtsev-Petviashvili system for the local Camassa-Holm hierarchy obtaining a candidate to the Baker-Akhiezer function for its first reduction generalizing the local Camassa-Holm. We focus our attention on the differences with…
We address the question regarding the structure of the Mitchell order on normal measures. We show that every well founded order can be realized as the Mitchell order on a measurable cardinal $\kappa$ from some large cardinal assumption.
We review our results, published, prepublished or unpublished, on the well-posedness of selected generalized Kadomtsev-Petviashvili hierarchies.
We construct a Grassmannian-like formulation for the potential KP-hierarchy including additional ``negative'' flows. Our approach will generalize the notion of a tau-function to include negative flows. We compare the resulting hierarchy…