Linear Stability Conditions for a First Order n-Dimensional Mapping

In this work, we investigate several models described by a single real scalar field with nonpolynomial interactions, constructed to support topological solutions. We do this using the deformation procedure to introduce a function which allows to construct two distinct families of hyperbolic potentials, controlled by three distinct parameters, in the standard formalism. In this way, the procedure allows us to get analytical solutions, and then investigate the energy density, linear stability and zero mode. We move on and introduce a nonstandard formalism to obtain compact solutions, analytically. We also investigate these hyperbolic models in the braneworld context, considering both the standard and nonstandard possibilities. The results show how to construct distinct braneworld models which are implemented via the first-order formalism and are stable against fluctuation of the metric tensor.

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Publisher's Note: Linear stability analysis of first-order delayed car-following models on a ring [Phys. Rev. E86, 036207 (2012)]

Physical Review E ◽

10.1103/physreve.87.069902 ◽

2013 ◽

Vol 87 (6) ◽

Author(s):

Antoine Tordeux ◽

Michel Roussignol ◽

Sylvain Lassarre

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Car Following ◽

First Order

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Linear stability and stability of syzygy bundles

International Journal of Mathematics ◽

10.1142/s0129167x18500805 ◽

2018 ◽

Vol 29 (11) ◽

pp. 1850080 ◽

Cited By ~ 1

Author(s):

Abel Castorena ◽

H. Torres-López

Keyword(s):

Exact Sequence ◽

Linear Stability ◽

Commutative Diagram ◽

Linear Series ◽

Stability Conditions ◽

Stable Bundle ◽

Projective Curve ◽

General Curve ◽

The Stability ◽

Natural Way

Let [Formula: see text] be a smooth irreducible projective curve and let [Formula: see text] be a complete and generated linear series on [Formula: see text]. Denote by [Formula: see text] the kernel of the evaluation map [Formula: see text]. The exact sequence [Formula: see text] fits into a commutative diagram that we call the Butler’s diagram. This diagram induces in a natural way a multiplication map on global sections [Formula: see text], where [Formula: see text] is a subspace and [Formula: see text] is the dual of a subbundle [Formula: see text]. When the subbundle [Formula: see text] is a stable bundle, we show that the map [Formula: see text] is surjective. When [Formula: see text] is a Brill–Noether general curve, we use the surjectivity of [Formula: see text] to give another proof of the semistability of [Formula: see text], moreover, we fill up a gap in some incomplete argument by Butler: With the surjectivity of [Formula: see text] we give conditions to determine the stability of [Formula: see text], and such conditions imply the well-known stability conditions for [Formula: see text] stated precisely by Butler. Finally we obtain the equivalence between the (semi)stability of [Formula: see text] and the linear (semi)stability of [Formula: see text] on [Formula: see text]-gonal curves.

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