Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schrodinger Equation on homogeneous trees   Let T be a homogeneous tree and L the Laplace operator on T. We consider the
semilinear Schrodinger equation associated to L with a power-like nonlinearity
F of degree d. We first obtain dispersive estimates and Strichartz estimates
with no admissibility conditions. We next deduce global well-posedness for
small L2 data with no gauge invariance assumption on the nonlinearity F. On the
other hand if F is gauge invariant, L2 conservation leads to global
well-posedness for arbitrary L2 data. Notice that, in contrast with the
Euclidean case, these global well-posedness results hold with no restriction on
d > 1. We finally prove scattering for small L2 data, with no gauge invariance
assumption.

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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int