Related papers: A new extended matrix KP hierarchy and its solutio…
A method is proposed to construct a new extended KP hierarchy, which includes two types of KP equation with self-consistent sources and admits reductions to k-constrained KP hierarchy and to Gelfand-Dickey hierarchy with sources. It…
A method is proposed in this paper to construct a new extended q-deformed KP ($q$-KP) hiearchy and its Lax representation. This new extended $q$-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its…
We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to…
Inspired by the squared eigenfunction symmetry constraint, we introduce a new $\ta_k$-flow by ``extending'' a specific $t_n$-flow of discrete KP hierarchy (DKPH). We construct extended discrete KPH (exDKPH), which consists of $t_n$-flow,…
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…
It is shown that the matrix KP hierarchy can yield new integrable equations in $(2+1)$-dimensions along with the corresponding Lax pair. For particular gauge choice this may result derivative and also a higher order nonlinear extension of…
We firstly propose two kinds of new multi-component BKP (mcBKP) hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources…
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…
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.…
We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained KP hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy, $(t_A,\tau_B)$ and $(\gamma_A,\sigma_B)$ matrix hierarchies.…
In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear…
The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with…
Based on the eigenfunction symmetry constraint of the q-deformed modified KP hierarchy, a q-deformed mKP hierarchy with self-consistent sources ($q$-mKPHSCSs) is constructed. The q-mKPHSCSs contains two types of q-deformed mKP equation with…
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…
A new (\gamma_n,\sigma_k)-KP hierarchy with two new time series \gamma_n and \sigma_k, which consists of \gamma_n-flow, \sigma_k-flow and mixed \gamma_n and \sigma_k evolution equations of eigenfunctions, is proposed. Two reductions and…
We present (2+1)-dimensional generalizations of the k-constrained Kadomtsev-Petviashvili (k-cKP) hierarchy and corresponding matrix Lax representations that consist of two integro-differential operators. Additional reductions imposed on the…
We present an affine $sl (n+1)$ algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax…
We show that any multi-component matrix KP hierarchy is equivalent to the standard one-component (scalar) KP hierarchy endowed with a special infinite set of abelian additional symmetries, generated by squared eigenfunction potentials. This…
Starting from free charged fermions we give equivalent definitions of the $n\/$-component KP hierarchy, in terms of $\tau\/$-functions $\tau_\alpha\/$ (where $\alpha \in M =\/$ root lattice of $sl_n\/$), in terms of $n \times n\/$ matrix…
A new infinite set of commuting additional (``ghost'') symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to…