Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic forms in the theory of solitons   We develop a Hamiltonian theory for 2D soliton equations. In particular, we
identify the spaces of doubly periodic operators on which a full hierarchy of
commuting flows can be introduced, and show that these flows are Hamiltonian
with respect to a universal symplectic form $\omega={1\over 2}\r_{\infty}
<\Psi_0^*\delta L\wedge\delta\Psi_0>\d k$. We also construct other higher order
symplectic forms and compare our formalism with the case of 1D solitons.
Restricted to spaces of finite-gap solitons, the universal symplectic form
agrees with the symplectic forms which have recently appeared in non-linear WKB
theory, topological field theory, and Seiberg-Witten theories. We take the
opportunity to survey some developments in these areas where symplectic forms
have played a major role.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph