Volume 13, Issue 2, May 2006, Pages 193 - 204
The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources
- Ting XIAO, Yunbo ZENG
- Corresponding Author
- Ting XIAO
Available Online 1 May 2006.
- https://doi.org/10.2991/jnmp.2006.13.2.4How to use a DOI?
- For the first time we show that the quasiclassical limit of the symmetry constraint of the Sato operator for the KP hierarchy leads to the generalized Zakharov reduction of the Sato function for the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry constraint of the dKP hierarchy recently. By either regarding the symmetry constrained dKP hierarchy as its stationary case or taking the dispersionless limit of the KP hierarchy with self-consistent sources directly, we construct a new integrable dispersionless hierarchy, i.e., the dKP hierarchy with self-consistent sources and find its associated conservation equations (or equations of Hamilton-Jacobi type). Some solutions of the dKP equation with self-consistent sources are also obtained by hodograph transformations.
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Cite this article
TY - JOUR AU - Ting XIAO AU - Yunbo ZENG PY - 2006 DA - 2006/05 TI - The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources JO - Journal of Nonlinear Mathematical Physics SP - 193 EP - 204 VL - 13 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2006.13.2.4 DO - https://doi.org/10.2991/jnmp.2006.13.2.4 ID - XIAO2006 ER -