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TMF, 2010, Volume 165, Number 2, Pages 257–271 (Mi tmf6575)  

Kernel formula approach to the universal Whitham hierarchy

Hsin-Fu Shena, Niann-Chern Leeb, Ming-Hsien Tuc

a Department of Mechanical Engineering, WuFeng Institute of Technology, Chiayi, Taiwan
b General Education Center, National Chinyi University of Technology, Taichung, Taiwan
c Department of Physics, National Chung Cheng University, Chiayi, Taiwan

Abstract: Based on the kernel formula proposed by Carroll and Kodama, we derive the dispersionless Hirota equations of the universal Whitham hierarchy. We also verify the associativity equations in this hierarchy from the dispersionless Hirota equations and give a realization of the associative algebra with the structure constants expressed in terms of residue formulas.

Keywords: kernel formula, Lax formulation, dispersionless Hirota equation, Whitham hierarchy, WDVV equation, residue formula

DOI: https://doi.org/10.4213/tmf6575

Full text: PDF file (434 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 165:2, 1456–1469

Bibliographic databases:

Document Type: Article
Received: 20.03.2010

Citation: Hsin-Fu Shen, Niann-Chern Lee, Ming-Hsien Tu, “Kernel formula approach to the universal Whitham hierarchy”, TMF, 165:2 (2010), 257–271; Theoret. and Math. Phys., 165:2 (2010), 1456–1469

Citation in format AMSBIB
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\paper Kernel formula~approach to the~universal Whitham hierarchy
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\issue 2
\pages 257--271
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\pages 1456--1469
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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