Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Algebro-Geometric Toda Hierarchy Initial Value Problem for
  Complex-Valued Initial Data   We discuss the algebro-geometric initial value problem for the Toda hierarchy
with complex-valued initial data and prove unique solvability globally in time
for a set of initial (Dirichlet divisor) data of full measure. To this effect
we develop a new algorithm for constructing stationary complex-valued
algebro-geometric solutions of the Toda hierarchy, which is of independent
interest as it solves the inverse algebro-geometric spectral problem for
generally non-self-adjoint Jacobi operators, starting from a suitably chosen
set of initial divisors of full measure. Combined with an appropriate
first-order system of differential equations with respect to time (a substitute
for the well-known Dubrovin equations), this yields the construction of global
algebro-geometric solutions of the time-dependent Toda hierarchy.
  The inherent non-self-adjointness of the underlying Lax (i.e., Jacobi)
operator associated with complex-valued coefficients for the Toda hierarchy
poses a variety of difficulties that, to the best of our knowledge, are
successfully overcome here for the first time. Our approach is not confined to
the Toda hierarchy but applies generally to 1+1-dimensional completely
integrable (discrete and continuous) soliton equations.

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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th