Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear and orbital stability analysis for solitary-wave solutions of
  variable-coefficient scalar field equations   We study general semilinear scalar-field equations on the real line with
variable coefficients in the linear terms. These coefficients are uniformly
small, but slowly decaying, perturbations of a constant-coefficient operator.
We are motivated by the question of how these perturbations of the equation may
change the stability properties of kink solutions (one-dimensional topological
solitons). We prove existence of a stationary kink solution in our setting, and
perform a detailed spectral analysis of the corresponding linearized operator,
based on perturbing the linearized operator around the constant-coefficient
kink. We derive a formula that allows us to check whether a discrete eigenvalue
emerges from the essential spectrum under this perturbation. Known examples
suggest that this extra eigenvalue may have an important influence on the
long-time dynamics in a neighborhood of the kink. We also establish orbital
stability of solitary-wave solutions in the variable-coefficient regime,
despite the possible presence of negative eigenvalues in the linearization.

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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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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: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol