On Kernel Formulas and Dispersionless Hirota Equations

Details On Kernel Formulas and Dispersionless Hirota Equations On Kernel Formulas and Dispersionless Hirota Equations

2006-05-23

arxiv.org/abs/nlin/0605042v2

J. Math. Phys. 47 (2006) 102702

Nonlinear Sciences

Exactly Solvable and Integrable Systems

30 pages, minor corrections, references added

Scientific paper

10.1063/1.2358002

We rederive dispersionless Hirota equations of the dispersionless Toda hierarchy from the method of kernel formula provided by Carroll and Kodama. We then apply the method to derive dispersionless Hirota equations of the extended dispersionless BKP(EdBKP) hierarchy proposed by Takasaki. Moreover, we verify associativity equations (WDVV equations) in the EdBKP hierarchy from dispersionless Hirota equations and give a realization of associative algebra with structure constants expressed in terms of residue formula.

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