The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources

DOI

10.2991/jnmp.2006.13.2.4How to use a DOI?

Abstract

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Ting Xiao
AU  - Yunbo Zeng
PY  - 2006
DA  - 2006/05/01
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  - 10.2991/jnmp.2006.13.2.4
ID  - Xiao2006
ER  -