A new extended KP hierarchy

Abstract

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 provides a general way to construct soliton equations with sources and their Lax representations.Comment: Published in Phys. Lett. A, 13 page

Two New Multi-component BKP Hierarchies

“…It is noticed that (2.38) is the coupled mKdV equation which has been obtained in [20] and that (2.39) is a new KdV equation with self-consistent sources which is completely different from the two known KdV equations with self-consistent sources introduced by [8,[21][22][23].…”

“…In this paper, following the idea in [8] and using the eigenfunction symmetry constraint, we firstly introduce a new type of Lax equations which consist of the new time τ k − flow and the evolutions of wave functions.…”

The Transformation between the AKNS Hierarchy and the KN Hierarchy with Self-Consistent Sources

“…Both hierarchies can be found in [23] and references therein. They have been studied through the constraint flows [11,23], source-generating approach [3,20] and introducing a new time variable in the frame of Sato' theory [12,15]. Several methods are used to solve those equations including the inverse scattering transform (IST) [1,2,11,23], Daboux transform [13,14,21,24], bilinear method [3,20,25,26], etc.…”

The KP hierarchy with self–consistent sources: construction, Wronskian solutions and bilinear identities

“…In order to find a unified framework to study the two types of SESCSs, a systematical method was proposed by the authors on the basis of Sato's theory [13]. This is a systematic method to generate the SESCSs, and can be used to study the case of BKP, CKP [22], q-deformed KP [10,11], and some other cases.…”