Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersive Geometric Curve Flows   The Hodge star mean curvature flow on a 3-dimension Riemannian or
pseudo-Riemannian manifold, the geometric Airy flow on a Riemannian manifold,
the Schrodingier flow on Hermitian manifolds, and the shape operator curve flow
on submanifolds are natural non-linear dispersive curve flows in geometric
analysis. A curve flow is integrable if the evolution equation of the local
differential invariants of a solution of the curve flow is a soliton equation.
For example, the Hodge star mean curvature flow on $R^3$ and on $R^{2,1}$, the
geometric Airy flow on $R^n$, the Schrodingier flow on compact Hermitian
symmetric spaces, and the shape operator curve flow on an Adjoint orbit of a
compact Lie group are integrable. In this paper, we give a survey of these
results, describe a systematic method to construct integrable curve flows from
Lax pairs of soliton equations, and discuss the Hamiltonian aspect and the
Cauchy problem of these curve flows.

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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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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: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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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: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th