arXiv subjects

Xiaojun Liu

Publications and source records attributed to Xiaojun Liu.

40 records · Page 3Linked to original sources

arXiv2007

Two new multi-component BKP hierarchies

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 which Lax representations are presented. The two mcBKP hierarchies both admit reductions to the $k-$constrained BKP hierarchy and to integrable (1+1)-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of bi-directional SK equations with self-consistent sources.

nlin.SI↗

arXiv2007

A new multi-component two dimensional Toda lattice hierarchy and two dimensional Toda lattice with self-consistent sources

We propose a new multi-component two-dimensional Toda lattice hierarchy (mc2dTLH) which includes two-dimensional Toda lattice equation with self-consistent sources (2dTLSCS) as the first non-trivial equation. The Lax representations for this mc2dTLH are presented. We construct a non-auto-Bäcklund Darboux transformation (DT) for 2dTLSCS by applying the method of variation of constant (MVC) to ordinary DT of 2dTLSCS. This non-auto-Bäcklund DT enables us to obtain various solutions such as solitons, rational solutions etc., to 2dTLSCS.

nlin.SI↗

arXiv2007

A new multi-component CKP hierarchy

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 $k$-constrained CKP hierarchy and to a (1+1)-dimensional soliton hierarchy with self-consistent source, which include two types of Kaup-Kuperschmidt equation with self-consistent sources and of bi-directional Kaup-Kuperschmidt equation with self-consistent sources.

nlin.SI↗

arXiv2005

On the Toda Lattice Equation with Self-Consistent Sources

The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.

nlin.SI↗