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

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  • Xiao, Ting
  • Zeng, Yunbo

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.

Suggested Citation

  • Xiao, Ting & Zeng, Yunbo, 2005. "A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 38-60.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:38-60
    DOI: 10.1016/j.physa.2005.02.043
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    References listed on IDEAS

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    1. Lin, Runliang & Zeng, Yunbo & Ma, Wen-Xiu, 2001. "Solving the KdV hierarchy with self-consistent sources by inverse scattering method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 287-298.
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    Cited by:

    1. Wang, Hong-Yan, 2009. "Commutativity of source generation procedure and Bäcklund transformation: A BKP equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 779-785.
    2. Gegenhasi, & Hu, Xing-Biao, 2007. "Integrability of a differential-difference KP equation with self-consistent sources," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 145-158.

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