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SIGMA 2 (2006), 057, 22 pages nlin.SI/0604003
https://doi.org/10.3842/SIGMA.2006.057
Dispersionless Hirota Equations of Two-Component BKP Hierarchy
Kanehisa Takasaki
Graduate School of Human and Environmental Studies,
Kyoto University, Yoshida, Sakyo, Kyoto 606-8501, Japan
Received April 04, 2006, in final form May 02, 2006; Published online May 31, 2006
Abstract
The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy).
Dispersionless limit of this multi-component
hierarchy is considered on the level of the τ-function.
The so called dispersionless Hirota equations are obtained from
the Hirota equations of the τ-function. These dispersionless
Hirota equations turn out to be equivalent to a system of
Hamilton-Jacobi equations. Other relevant equations, in
particular, dispersionless Lax equations, can be derived from
these fundamental equations. For comparison, another approach
based on auxiliary linear equations is also presented.
Key words:
BKP hierarchy; Hirota equation; dispersionless limit.
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