A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources

Ting Xiao and Yunbo Zeng

Physica A: Statistical Mechanics and its Applications, 2005, vol. 353, issue C, 38-60

Abstract: 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 generalized Darboux transformation with arbitrary functions in time t for the mKPESCS which, in contrast with the Darboux transformation for the mKP equation, provides a nonauto-Bäcklund transformation between two mKPESCSs with different degrees. The formula for n-times repeated generalized Darboux transformation is proposed and enables us to find the rational solutions (including the lump solutions), soliton solutions and the solutions of breather type of the mKPESCS.

Keywords: Lax representation; Constrained mKP hierarchy; mKP equation with self-consistent sources (mKPESCS); Darboux transformation (DT); Rational solution; Soliton solution; Solution of breather type (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437105001056
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:353:y:2005:i:c:p:38-60

DOI: 10.1016/j.physa.2005.02.043

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().