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On kernel formulas and dispersionless hirota equations of the extended dispersionless bkp hierarchy. (English) Zbl 1112.37055

Summary: We derive dispersionless Hirota equations of the extended dispersionless BKP (EdBKP) hierarchy proposed by Takasaki from the method of kernel formula provided by Carroll and Kodama. 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 the residue formula.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
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