56 research outputs found
Statistical theory of the excited strip domain structure
A statistical theory of the strip domain structure excited in a bubble film
by an oscillating magnetic field is developed. The theory is based on the
consideration of the strip domain structure as a thermodynamic system
characterized by the spectrum of domain walls oscillation and an effective
temperature that is caused by an oscillating magnetic field and film
nonuniformities. We found the thermodynamic characteristics of that domain
structure and calculated its period as a function of the frequency and
amplitude of an oscillating magnetic field.Comment: 6 pages, 3 figure
Nonlinear Schr\"odinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
In this paper, we construct a generalized Darboux transformation for
nonlinear Schr\"odinger equation. The associated -fold Darboux
transformation is given both in terms of a summation formula and in terms of
determinants. As applications, we obtain compact representations for the -th
order rogue wave solutions of the focusing nonlinear Schr\"odinger equation and
Hirota equation. In particular, the dynamics of the general third order rogue
wave is discussed and shown to exhibit interesting structure.Comment: 17 pages, 4 figures, replaced by revised versio
On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices
We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.Comment: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press
Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets
A parametrically forced sine-Gordon equation with a fast periodic {\em
mean-zero} forcing is considered. It is shown that -kinks represent a
class of solitary-wave solutions of the equation. This result is applied to
quasi-one-dimensional ferromagnets with an easy plane anisotropy, in a rapidly
oscillating magnetic field. In this case the -kink solution we have
introduced corresponds to the uniform ``true'' domain wall motion, since the
magnetization directions on opposite sides of the wall are anti-parallel. In
contrast to previous work, no additional anisotropy is required to obtain a
true domain wall. Numerical simulations showed good qualitative agreement with
the theory.Comment: 3 pages, 1 figure, revte
Discrete Breathers
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the
form of discrete breathers. These solutions are time-periodic and (typically
exponentially) localized in space. The lattices exhibit discrete translational
symmetry. Discrete breathers are not confined to certain lattice dimensions.
Necessary ingredients for their occurence are the existence of upper bounds on
the phonon spectrum (of small fluctuations around the groundstate) of the
system as well as the nonlinearity in the differential equations. We will
present existence proofs, formulate necessary existence conditions, and discuss
structural stability of discrete breathers. The following results will be also
discussed: the creation of breathers through tangent bifurcation of band edge
plane waves; dynamical stability; details of the spatial decay; numerical
methods of obtaining breathers; interaction of breathers with phonons and
electrons; movability; influence of the lattice dimension on discrete breather
properties; quantum lattices - quantum breathers. Finally we will formulate a
new conceptual aproach capable of predicting whether discrete breather exist
for a given system or not, without actually solving for the breather. We
discuss potential applications in lattice dynamics of solids (especially
molecular crystals), selective bond excitations in large molecules, dynamical
properties of coupled arrays of Josephson junctions, and localization of
electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see
also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm
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