B1) M. Cadoni, R. De Leo and S. Demelio, Soliton propagation in homogeneous and
inhomogeneous models for DNA torsion dynamics, J. Nonlin. Math. Phys. 18, suppl.
2, 287-319, 2011

The existence of solitonic excitations is a generic feature of a broad class of
homogeneous models for nonlinear DNA internal torsional dynamics, but many
properties of solitonic propagation depend on the actual model one is
considering. In this paper we perform a detailed and comparative numerical
investigation of the profiles and time evolution of solitons for two different
models, the Yakushevich one and the more recent "composite" model of [1], and
for two different choices of the potential describing the pairing interaction
between bases (harmonic and Morse potential). We consider not only homogeneous
DNA chains but also inhomogeneous ones (with sequence of bases corresponding to
a real organism, the Human Adenovirus 2). We show that twist solitons can
propagate in inhomogeneous chains over biologically significant distances. It is
also shown that stable soliton propagation is possible for inhomogeneous chains
when dissipation and an external force are present. On a more general level, our
results indicate that solitonic propagation can take place in highly
inhomogeneous nonlinear media. 

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B2) M. Cadoni, R. De Leo, S. Demelio and G. Gaeta, Propagation of twist solitons
in fully inhomogeneous dna chains, J. Nonlin. Math. Phys. 17, 567-569, 2010

In the framework of a recently introduced model of DNA torsional dynamics, we
argued on the basis of perturbative considerations that an inhomogeneous DNA
chain could support long-lived soliton-type excitations due to the peculiar
geometric structure of DNA and the effect of this on nonlinear torsional
dynamics. Here we consider an inhomogeneous version of this model of DNA
torsional dynamics, and investigate numerically the propagation of solitons in
a DNA chain with a real base sequence (corresponding to the Human Adenovirus 2);
this implies inhomogeneities of up to 50% in the base masses and inter-pair
interactions. We find that twist solitons propagate for considerable distances
(210 times their diameters) before stopping due to phonon emission. Our results
show that twist solitons may exist in realistic DNA chain models, and on a more
general level that solitonic propagation can take place in highly inhomogeneous
media. The most relevant feature for general nonlinear dynamics is that we
identify the physical mechanisms allowing this behavior and thus the class of
models candidate to support long-lived soliton-type excitations in the presence
of significant inhomogeneities.

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B3) M. Cadoni, R. De Leo, S. Demelio and G. Gaeta, Twist solitons in complex
macromolecules: From DNA to polyethylene, Int. J. Nonlin. Mech. 43, 1094-1107,
2008

DNA torsion dynamics is essential in the transcription process; simple models
for it have been proposed by several authors, in particular Yakushevich
(Y model). These are strongly related to models of DNA separation dynamics such
as the one first proposed by Peyrard and Bishop (and developed by Dauxois,
Barbi, Cocco and Monasson among others), but support topological solitons. We
recently developed a "composite" version of the Y model, in which the
sugar-phosphate group and the base are described by separate degrees of freedom.
This at the same time fits experimental data better than the simple Y model, and
shows dynamical phenomena, which are of interest beyond DNA dynamics. Of
particular relevance are the mechanism for selecting the speed of solitons by
tuning the physical parameters of the non-linear medium and the hierarchal
separation of the relevant degrees of freedom in "master" and "slave". These
mechanisms apply not only do DNA, but also to more general macromolecules, as
we show concretely by considering polyethylene.

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B4) M. CADONI M, DE LEO R, GAETA G (2007). Solitons in a double pendulums chain
model, and DNA roto-torsional dynamics. JOURNAL OF NONLINEAR MATHEMATICAL
PHYSICS, vol. 14, p. 128-146.

It was first suggested by Englander et al to model the nonlinear dynamics of DNA
relevant to the transcription process in terms of a chain of coupled pendulums.
In a related paper [4] we argued for the advantages of an extension of this
approach based on considering a chain of double pendulums with certain
characteristics. Here we study a simplified model of this kind, focusing on its
general features and nonlinear travelling wave excitations; in particular, we
show that some of the degrees of freedom are actually slaved to others, allowing
for an effective reduction of the relevant equations.

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B5) M. Cadoni, R. De Leo and G. Gaeta, Sine-Gordon solitons, auxiliary fields
and singular limit of a double pendulums chain, J. Phys. A 40, 12917-12929, 2007

We consider the continuum version of an elastic chain supporting topological and
non-topological degrees of freedom; this generalizes a model for the dynamics of
DNA recently proposed and investigated by ourselves. In a certain limit, the
non-topological degrees of freedom are frozen, and the model reduces to the
sine-Gordon equations and thus supports well-known topological soliton
solutions. We consider a (singular) perturbative expansion around this limit and
study in particular how the non-topological field assumes the role of
an auxiliary field. This provides a more general framework for the slaving of
this degree of freedom on the topological one, already observed elsewhere in the
context of the mentioned DNA model; in this framework one expects such
a phenomenon to arise in a quite large class of field-theoretical models.

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B6) CADONI M, DE LEO R, GAETA G (2007). A Symmetry breaking mechanism for
selecting the speed of relativistic solitons. JOURNAL OF PHYSICS. A,
MATHEMATICAL AND THEORETICAL, vol. A40, p. 8517-8534.

We propose a mechanism for fixing the velocity of relativistic solitons based on
the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal
is first elaborated for a molecular chain model as the simple pendulum limit of
a double pendulums chain. It is then generalized to a full class of
two-dimensional field theories of the sine-Gordon type. From a phenomenological
point of view, the mechanism allows one to select the speed of a SG soliton just
by tuning elastic couplings constants and kinematical parameters. From
a fundamental, field-theoretical point of view we show that the characterizing
features of relativistic SG solitons (existence of conserved topological charges
and stability) may be still preserved even if the Lorentz symmetry is broken and
a soliton of a given speed is selected.

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B7) M. Cadoni, R. De Leo and G. Gaeta, Composite model for DNA torsion dynamics,
Phys. Rev. E 75 (2007), 021919

DNA torsion dynamics is essential in the transcription process; a simple model
for it, in reasonable agreement with experimental observations, has been
proposed by Yakushevich (Y) and developed by several authors; in this, the
nucleotides (the DNA subunits made of a sugar-phosphate group and the attached
nitrogen base) are described by a single degree of freedom. In this paper we
propose and investigate, both analytically and numerically, a "composite"
version of the Y model, in which the sugar-phosphate group and the base are
described by separate degrees of freedom. The model proposed here contains as
a particular case the Y model and shares with it many features and results, but
represents an improvement from both the conceptual and the phenomenological
point of view. It provides a more realistic description of DNA and possibly
a justification for the use of models which consider the DNA chain as uniform.
It shows that the existence of solitons is a generic feature of the underlying
nonlinear dynamics and is to a large extent independent of the detailed modeling
of DNA. The model we consider supports solitonic solutions, qualitatively and
quantitatively very similar to the Y solitons, in a fully realistic range of all
the physical parameters characterizing the DNA. 

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B8) Cadoni M (1998). 2D extremal black holes as solitons. PHYSICAL REVIEW D 58,
1040011-1040017

We discuss the relationship between two-dimensional (2D) dilaton gravity models
and sine-Gordon-like field theories. We show that there is a one-to-one
correspondence between the solutions of 2D dilaton gravity and the solutions of
a (two fields) generalization of the sine-Gordon model. In particular, we find
a connection between the soliton solutions of the generalized sine-Gordon model
and extremal black hole solutions of 2D dilaton gravity. As a by-product of our
calculations we find an easy way to generate cosmological solutions of 2D
dilaton gravity.

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B9) Cadoni M, Mignemi S, Serra M (2012). Black brane solutions and their
solitonic extremal limit in Einstein-scalar gravity. PHYSICAL REVIEW D,
PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY 85, 086001

We investigate static, planar solutions of Einstein-scalar gravity admitting
an anti-de-Sitter (AdS) vacuum. When the squared mass of the scalar field is
positive and the scalar potential can be derived from a superpotential, minimum
energy theorems indicate the existence of a scalar soliton. On the other hand,
for these models, no-hair theorems forbid the existence of hairy black brane
solutions with AdS asymptotics. By considering a specific example (an exact
integrable model which has the form of a Toda molecule) and by deriving explicit
exact solution, we show that these models allow for hairy black brane solutions
with non-AdS domain wall asymptotics, whose extremal limit is a scalar soliton.
The soliton smoothly interpolates between a non-AdS domain wall solution at r=δ
and an AdS solution near r=0.

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B10) Cadoni M, Mignemi S, Serra M (2011). Exact solutions with AdS asymptotics
of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field.
PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY 84, 084046

We propose a general method for solving exactly the static field equations of
Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our
method starts from an ansatz for the scalar field profile, and determines,
together with the metric functions, the corresponding form of the scalar
self-interaction potential. Using this method we prove a new no-hair theorem
about the existence of hairy black-hole and black-brane solutions and derive
broad classes of static solutions with radial symmetry of the theory, which may
play an important role in applications of the AdS/CFT correspondence to
condensed matter and strongly coupled QFTs. These solutions include: (1) four-
or generic (d+2)-dimensional solutions with planar, spherical or hyperbolic
horizon topology; (2)solutions with anti-deSitter, domain wall and Lifshitz
asymptotics; (3)solutions interpolating between an anti-deSitter spacetime in
the asymptotic region and a domain wall or conformal Lifshitz spacetime in the
near-horizon region.