429 research outputs found
Helmholtz solitons in power-law optical materials
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures broad beam evolution at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses and liquid crystals. Novel exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three conservation laws are also reported and numerical simulations examine the stability of the Helmholtz power-law solitons. These simulations have led to the identification of a new propagation feature associated with spatial solitons in power-law media, constituting a new class of oscillatory solution
Problem of a quantum particle in a random potential on a line revisited
The density of states for a particle moving in a random potential with a
Gaussian correlator is calculated exactly using the functional integral
technique. It is achieved by expressing the functional degrees of freedom in
terms of the spectral variables and the parameters of isospectral
transformations of the potential. These transformations are given explicitly by
the flows of the Korteweg-de Vries hierarchy which deform the potential leaving
all its spectral properties invariant. Making use of conservation laws reduces
the initial Feynman integral to a combination of quadratures which can be
readily calculated. Different formulations of the problem are analyzed.Comment: 11 pages, RevTex, preprint ANU-RSPhySE-20994 (comment added
Maxwell-Drude-Bloch dissipative few-cycle optical solitons
We study the propagation of few-cycle pulses in two-component medium
consisting of nonlinear amplifying and absorbing two-level centers embedded
into a linear and conductive host material. First we present a linear theory of
propagation of short pulses in a purely conductive material, and demonstrate
the diffusive behavior for the evolution of the low-frequency components of the
magnetic field in the case of relatively strong conductivity. Then, numerical
simulations carried out in the frame of the full nonlinear theory involving the
Maxwell-Drude-Bloch model reveal the stable creation and propagation of
few-cycle dissipative solitons under excitation by incident femtosecond optical
pulses of relatively high energies. The broadband losses that are introduced by
the medium conductivity represent the main stabilization mechanism for the
dissipative few-cycle solitons.Comment: 38 pages, 10 figures. submitted to Physical Review
On the Integrability of the Discrete Nonlinear Schroedinger Equation
In this letter we present an analytic evidence of the non-integrability of
the discrete nonlinear Schroedinger equation, a well-known discrete evolution
equation which has been obtained in various contexts of physics and biology. We
use a reductive perturbation technique to show an obstruction to its
integrability.Comment: 4 pages, accepted in EP
Applications of Solvable Lie Algebras to a Class of Third Order Equations
A family of third-order partial differential equations (PDEs) is analyzed. This family
broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and
the Burgers equation, which model many real-world phenomena. Furthermore, several macroscopic
models for semiconductors considering quantum effects—for example, models for the transmission of
electrical lines and quantum hydrodynamic models—are governed by third-order PDEs of this family.
For this family, all point symmetries have been derived. These symmetries are used to determine
group-invariant solutions from three-dimensional solvable subgroups of the complete symmetry
group, which allow us to reduce the given PDE to a first-order nonlinear ordinary differential equation
(ODE). Finally, exact solutions are obtained by solving the first-order nonlinear ODEs or by taking
into account the Type-II hidden symmetries that appear in the reduced second-order ODEs
Multiscale reduction of discrete nonlinear Schroedinger equations
We use a discrete multiscale analysis to study the asymptotic integrability
of differential-difference equations. In particular, we show that multiscale
perturbation techniques provide an analytic tool to derive necessary
integrability conditions for two well-known discretizations of the nonlinear
Schroedinger equation.Comment: 12 page
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