Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Grassmannian flows and applications to nonlinear partial differential
  equations   We show how solutions to a large class of partial differential equations with
nonlocal Riccati-type nonlinearities can be generated from the corresponding
linearized equations, from arbitrary initial data. It is well known that
evolutionary matrix Riccati equations can be generated by projecting linear
evolutionary flows on a Stiefel manifold onto a coordinate chart of the
underlying Grassmann manifold. Our method relies on extending this idea to the
infinite dimensional case. The key is an integral equation analogous to the
Marchenko equation in integrable systems, that represents the coodinate chart
map. We show explicitly how to generate such solutions to scalar partial
differential equations of arbitrary order with nonlocal quadratic
nonlinearities using our approach. We provide numerical simulations that
demonstrate the generation of solutions to
Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal
nonlinearities. We also indicate how the method might extend to more general
classes of nonlinear partial differential systems.

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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph