On Kernel Formulas and Dispersionless Hirota Equations

Abstract

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.

30 pages, minor corrections, references added

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Cited by in corpus (9)

• Combinatorics of dispersionless integrable systems and universality in random matrix theory
• Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
• On Kernel Formulas and Dispersionless Hirota Equations
• Differential Fay identities and auxiliary linear problem of integrable hiearchies
• Bihamiltonian Structure of the Two-component Kadomtsev-Petviashvili Hierarchy of type B
• Loewner equations, Hirota equations and reductions of universal Whitham hierarchy
• A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds
• Kernel Formula Approach to the Universal Whitham Hierarchy
• Solutions for real dispersionless Veselov-Novikov hierarchy