Related papers: Nonlocal symmetries for bilinear equations and the…
A difference analogue of the logistic equation, which preserves integrability, is derived from Hirota's bilinear difference equation. The integrability of the map is shown to result from the large symmetry associated with the B\"acklund…
Hirota's bilinear approach is a very effective method to construct solutions for soliton systems. In terms of this method, the nonlinear equations can be transformed into linear equations, and can be solved by using perturbation method. In…
In this paper we study systematically the question of supersymmetrization of the non-local gas equation. We obtain both the N=1 and the N=2 supersymmetric generalizations of the system which are integrable. We show that both the systems are…
We introduce a single tau function that represents the CKP hierarchy into a generalized Hirota "bilinear" equation. The actions on the tau function by additional symmetries for the hierarchy are calculated, which involve strictly more than…
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models ${\sl cKP}_{R,M}$, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an…
We study additional non-isospectral symmetries of constrained (reduced) N=2 supersymmetric KP hierarchies of integrable ``soliton''-like evolution equations. These symmetries are shown to form an infinite-dimensional non-Abelian superloop…
General soliton solutions to a nonlocal nonlinear Schr\"odinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions {are considered} via the combination of Hirota's bilinear method and the Kadomtsev-Petviashvili…
A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-$N$ limit of…
We describe three different approaches to the extended (N=2) supersymmetrization of the multicomponent KP hierarchy. In the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as…
We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…
In this paper, we construct the bilinear identities for the wave functions of an extended Kadomtsev-Petviashvili (KP) hierarchy, which is the KP hierarchy with particular extended flows (2008, Phys. Lett. A, 372: 3819). By introducing an…
Recently, Lembert, Gilson et al proposed a lucid and systematic approach to obtain bilinear B\"{a}cklund transformations and Lax pairs for constant-coefficient soliton equations based on the use of binary Bell polynomials. In this paper, we…
In this paper, we review various properties of the supersymmetric Two Boson (sTB) system. We discuss the equation and its nonstandard Lax representation. We construct the local conserved charges as well as the Hamiltoniam structures of the…
Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each…
A new quantile regression concept, based on a directional version of Koenker and Bassett's traditional single-output one, has been introduced in [Ann. Statist. (2010) 38 635-669] for multiple-output location/linear regression problems. The…
We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of $W_n$…
In this paper, we study two generalized constrained integrable hierarchies, which are called the $c$-$k$ constrained KP and BKP hierarchies. The Fermionic picture of the $c$-$k$ constrained KP hierarchy is given. We give some solutions for…
Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax…
A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for…
We consider the Schwarzian KP and Harry Dym hierarchies in the framework of the bilinear formalism which is well known for such integrable hierarchies as KP, modified KP, BKP, Toda lattice and other. We show that, similarly to the bilinear…