Related papers: A note on the modified KP hierarchy and its (yet a…
In this paper we revisit the subject of stationary flows of Lax hierarchies of a coupled KdV class. We explain the main ideas in the standard KdV case and then consider the dispersive water waves (DWW) case, with respectively 2 and 3…
We give 4 formulations of the Modified KP hierarchy and show that they are equivalent. We also discuss the reductions of the MKP hierarchy to the modified $n$-KdV hierarchies. As a byproduct, we find an astonishingly simple explicit…
Rational Lax hierarchies introduced by Krichever are generalized. A systematic construction of infinite multi-Hamiltonian hierarchies and related conserved quantities is presented. The method is based on the classical R-matrix approach…
A pluri-Lagrangian (or Lagrangian multiform) structure is an attribute of integrability that has mainly been studied in the context of multidimensionally consistent lattice equations. It unifies multidimensional consistency with the…
Solutions of a generalized constrained discrete KP (gcdKP) hierarchy with constraint on Lax operator $L^k=(L^k)_{\geq m}+\sum_{i=1}^lq_i\Delta^{-1}\Lambda^mr_i$, are invesitigated by Darboux transformations $T_D(f)=f^{[1]}\cdot\Delta\cdot…
In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting multi-folds quantum torus type Lie algebra. By a reduction, we also construct the…
We propose one possible generalization of the KP hierarchy, which possesses multi bi--hamiltonian structures, and can be viewed as several KP hierarchies coupled together.
We introduce the discrete hierarchy which naturally generalizes well known discrete KP hierarchy.
A space discretization of an integrable long wave-short wave interaction model, called the Yajima-Oikawa system, was proposed in the recent paper arXiv:1509.06996 using the Hirota bilinear method (see also…
We examine the conformal property of the second Hamiltonian structure of constrained KP hierarchy derived by Oevel and Strampp. We find that it naturallygives a family of nonlocal extended conformal algebras. We give two examples of such…
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 introduce a class of integrable $l$-field first-order lattices together with corresponding Lax equations. These lattices may be represented as consistency condition for auxiliary linear systems defined on sequences of formal dressing…
We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation respectively. Among these equations,…
In this paper, we present a new hierarchy which includes the intermediate long wave (ILW) equation at the lowest order. This hierarchy is thought to be a novel reduction of the 1st modified KP type hierarchy. The framework of our…
An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to…
This paper is devoted to the systematic study of additional (non- isospectral) symmetries of constrained (reduced) supersymmetric integrable hierarchies of KP type- the so called SKP_(R;M_B,M_F) models. The latter are supersymmetric…
We introduce a collection of nonlinear integrable partial differential-difference equations that are satisfied by the one-point distribution functions of some classical integrable KPZ models. Moreover, these equations can be regarded as…
A combination of dressing method and variation of constants as well as a formula for constructing the eigenfunction is used to solve the extended KP hierarchy, which is a hierarchy with one more series of time-flow and based on the symmetry…
The "pseudodual" of Ward's modified chiral model is a dispersionless limit of the matrix Kadomtsev-Petviashvili (KP) equation. This relation allows to carry solution techniques from KP over to the former model. In particular, lump solutions…
We apply the new method for constructing integrable Hamiltonian hierarchies of Lax type equations developed in our previous paper, to show that all W-algebras W(gl_N,f) carry such a hierarchy. As an application, we show that all vector…