mKP hierarchies with self-consistent sources
نویسندگان
چکیده
Using gauge transformations for the corresponding generating pseudo-differential operators L in terms of eigenfunctions and adjoint eigenfunctions, we construct several types of auto-Bäcklund transformations for the KP hierarchy with self-consistent sources (KPHSCS) and mKP hierarchy with self-consistent sources (mKPHSCS) respectively. The Bäcklund transformations from the KPHSCS to mKPHSCS are also constructed in this way. PACS number: 02.30.IK
منابع مشابه
Bäcklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources
The Bäcklund transformations between the constrained dispersionless KP hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH) and between the dispersionless KP hieararchy with self-consistent sources (dKPHSCS) and the dispersionless mKP hieararchy with self-consistent sources (dmKPHSCS) are constructed. The auto-Bäcklund transformations for the cdmKPH and for the dmKPHSCS ...
متن کاملThe constrained dispersionless mKP hierarchy and the dispersionless mKP hierarchy with self-consistent sources
We first show that the quasiclassical limit of the squared eigenfunction symmetry constraint of the Sato operator for the mKP hierarchy leads to a reduction of the Sato function for the dispersionless mKP hierarchy. The constrained dispersionless mKP hierarchy (cdmKPH) is obtained and it is shown that the (2+1)-dimensional dispersionless mKP hierarchy is decomposed to two (1+1)-dimensional hier...
متن کاملmKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources
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 self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generali...
متن کاملar X iv : 0 71 1 . 04 90 v 1 [ nl in . S I ] 4 N ov 2 00 7 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)-dimensiona...
متن کاملNonlinear Bi-Integrable Couplings of Multicomponent Guo Hierarchy with Self-Consistent Sources
Based on a well-known Lie algebra, the multicomponent Guo hierarchy with self-consistent sources is proposed. With the help of a set of non-semisimple Lie algebra, the nonlinear biintegrable couplings of the multicomponent Guo hierarchy with self-consistent sources are obtained. It enriches the content of the integrable couplings of hierarchies with self-consistent sources. Finally, the Hamilto...
متن کامل