Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric discrete AKP and BKP equations   We show that when KP (Kadomtsev-Petviashvili) $\tau$ functions allow special
symmetries, the discrete BKP equation can be expressed as a linear combination
of the discrete AKP equation and its reflected symmetric forms. Thus the
discrete AKP and BKP equations can share the same $\tau$ functions with these
symmetries. Such a connection is extended to 4 dimensional (i.e. higher order)
discrete AKP and BKP equations in the corresponding discrete hierarchies.
Various explicit forms of such $\tau$ functions, including Hirota's form,
Gramian, Casoratian and polynomial, are given. Symmetric $\tau$ functions of
Cauchy matrix form that are composed of Weierstrass $\sigma$ functions are
investigated. As a result we obtain a discrete BKP equation with elliptic
coefficients.

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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an