Related papers: n-th discrete KP hierarchy
A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
We propose a consistently algebraic formulation of the extended KP (supersymmetric) integrable -hierarchy systems. We exploit the results already established in [14] and which consist in a framework suspected to unify in a fascinating way…
For the first time we show that the quasiclassical limit of the symmetry constraint of the KP hierarchy leads to the generalized Zakharov reduction of the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry…
Two graphs are of the same topological type if they can be mutually embedded into each other topologically. We show that there are exactly $\aleph_1$ distinct topological types of countable trees. In general, for any infinite cardinal…
The recently proposed supersymmetric extensions of reduced Kadomtsev-Petviashvili (KP) integrable hierarchies in $N =1,2$ superspace are shown to contain in the purely bosonic limit new types of ordinary non-supersymmetric integrable…
A relationship between Painleve systems and infinite-dimensional integrable hierarchies is studied. We derive a class of higher order Painleve systems from Drinfeld-Sokolov (DS) hierarchies of type A by similarity reductions. This result…
We consider a finite universe U (more exactly - a family U of them) and second order quantifiers Q_K, where for each U this means quantifying over a family of n(K)-place relations closed under permuting U. We define some natural orders and…
New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of $(2+1)$-dimensional integrable equations, including the DS-III equation and the $N$-wave problem.…
Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple system has finite dimension and give an explicit presentation…
We introduce a new generalization of matrix (1+1)-dimensional k-constrained KP hierarchy. The new hierarchy contains matrix generalizations of stationary DS systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik…
A $\bar{\partial}$-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane are described and some clases of explicit solutions of the…
We show that it is consistent that for some uncountable cardinal k, all compactifications of the countable discrete space with remainders homeomorphic to $D^k$ are homeomorphic to each other. On the other hand, there are $2^c$ pairwise…
The existence of decomposition solutions of the well-known nonlinear BKP hierarchy is explored. It is shown that these decompositions provide simple and interesting relationships between classical integrable systems and the BKP hierarchy.…
We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is…
We construct a good compactification of the variety of irreducible projective plane curves of degree n with d nodes and no other singularities.
We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.
In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.
Based on the analytic property of the symmetric $q$-exponent $e_q(x)$, a new symmetric $q$-deformed Kadomtsev-Petviashvili ($q$-KP) hierarchy associated with the symmetric $q$-derivative operator $\partial_q$ is constructed. Furthermore,…
We determine the finite groups whose real irreducible representations have different degrees.