Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Backlund transformation and L2-stability of NLS solitons   Ground states of a L2-subcritical focusing nonlinear Schrodinger (NLS)
equation are known to be orbitally stable in the energy class H1 thanks to its
variational characterization. In this paper, we will show L2-orbital stability
of 1-solitons to a one-dimensional cubic NLS equation for any initial data
which are close to 1-solitons in L2. Moreover, we prove that if the initial
data are in H3 in addition to being small in L2, then the solution remains in
an L2-neighborhood of a specific 1-soliton solution for all the time. The proof
relies on the Backlund transformation between zero and soliton solutions of
this integrable equation.

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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol