Volume 23, Issue 3, June 2016, Pages 383 - 398
New extension of dispersionless Harry Dym hierarchy
Authors
Hongxia Wu
Department of Mathematics, School of Sciences, Jimei University, Xiamen, 361021, PR China
Department of Mathematics, The University of Texas Rio Grande Valley, Edinburg, 78539, USA,wuhongxia@jmu.edu.cn.
Jingxin Liu, Yunbo Zeng
Department of Mathematics, Tsinghua University, Beijing, 100084, PR China,yzeng@math.tsinghua.edu.cn
Received 10 March 2016, Accepted 12 May 2016, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1199499How to use a DOI?
- Keywords
- Symmetry constraint; Extended dispersionless Harry Dym hierarchy; Dispersionless Harry Dym equation with self-consistent sources; Hodograph solutions; Bäcklund transformation
- Abstract
The symmetry constraint for dispersionless Harry Dym (dHD) hierarchy is derived for the first time by taking dispersionless limit of that for 2+1 dimensional Harry Dym hierarchy. Then, the dHD is extended by means of the symmetry constraint which we derived. From the zero-curvature equation of the new extended dHD hierarchy, two types of dHD equations with self-consistent sources (dHDESCS) together with their associated conservation equations are obtained. Moreover, the hodograph solutions to the first type of dHDESCS are given. Finally, Bäcklund transformation between the extended dispersionless mKP hierarchy and extended dHD Hierarchy are also constructed.
- Copyright
- © 2016 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Hongxia Wu AU - Jingxin Liu AU - Yunbo Zeng PY - 2021 DA - 2021/01/06 TI - New extension of dispersionless Harry Dym hierarchy JO - Journal of Nonlinear Mathematical Physics SP - 383 EP - 398 VL - 23 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1199499 DO - 10.1080/14029251.2016.1199499 ID - Wu2021 ER -