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Advances in Mathematical Physics
Volume 2015, Article ID 392723, 11 pages
http://dx.doi.org/10.1155/2015/392723
Research Article

Links between -KP Hierarchy, -mKP Hierarchy, and (2+1)--Harry Dym Hierarchy

1School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
2Department of Applied Mathematics, China Agricultural University, Beijing 100083, China
3Department of Mathematical Science, Tsinghua University, Beijing 100084, China

Received 12 July 2015; Accepted 16 November 2015

Academic Editor: Boris G. Konopelchenko

Copyright © 2015 Yehui Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The new (2+1)--Harry Dym hierarchy and -mKP hierarchy with two new time series and , which consist of -flow, -flow, and mixed and evolution equations of eigenfunctions, are proposed. Gauge transformations and reciprocal transformations between -KP hierarchy, -mKP hierarchy, and (2+1)--Harry Dym hierarchy are studied. Their soliton solutions are presented.