Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On billiard weak solutions of nonlinear PDE's and Toda flows   A certain class of partial differential equations possesses singular
solutions having discontinuous first derivatives ("peakons"). The time
evolution of peaks of such solutions is governed by a finite dimensional
completely integrable system. Explicit solutions of this system are constructed
by using algebraic-geometric method which casts it as a flow on an appropriate
Riemann surface and reduces it to a classical Jacobi inversion problem. The
algebraic structure of the finite dimensional flow is also examined in the
context of the Toda flow hierarchy. Generalized peakon systems are obtained for
any simple Lie algebra and their complete integrability is demonstrated.

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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: funct-an