6,289 research outputs found
Group properties and invariant solutions of a sixth-order thin film equation in viscous fluid
Using group theoretical methods, we analyze the generalization of a
one-dimensional sixth-order thin film equation which arises in considering the
motion of a thin film of viscous fluid driven by an overlying elastic plate.
The most general Lie group classification of point symmetries, its Lie algebra,
and the equivalence group are obtained. Similar reductions are performed and
invariant solutions are constructed. It is found that some similarity solutions
are of great physical interest such as sink and source solutions,
travelling-wave solutions, waiting-time solutions, and blow-up solutions.Comment: 8 page
Cheng Equation: A Revisit Through Symmetry Analysis
The symmetry analysis of the Cheng Equation is performed. The Cheng Equation
is reduced to a first-order equation of either Abel's Equations, the analytic
solution of which is given in terms of special functions. Moreover, for a
particular symmetry the system is reduced to the Riccati Equation or to the
linear nonhomogeneous equation of Euler type. Henceforth, the general solution
of the Cheng Equation with the use of the Lie theory is discussed, as also the
application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae
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Localization and Pattern Formation in Quantum Physics. II. Waveletons in Quantum Ensembles
In this second part we present a set of methods, analytical and numerical,
which can describe behaviour in (non) equilibrium ensembles, both classical and
quantum, especially in the complex systems, where the standard approaches
cannot be applied. The key points demonstrating advantages of this approach
are: (i) effects of localization of possible quantum states; (ii) effects of
non-perturbative multiscales which cannot be calculated by means of
perturbation approaches; (iii) effects of formation of complex/collective
quantum patterns from localized modes and classification and possible control
of the full zoo of quantum states, including (meta) stable localized patterns
(waveletons). We demonstrate the appearance of nontrivial localized (meta)
stable states/patterns in a number of collective models covered by the
(quantum)/(master) hierarchy of Wigner-von Neumann-Moyal-Lindblad equations,
which are the result of ``wignerization'' procedure (Weyl-Wigner-Moyal
quantization) of classical BBGKY kinetic hierarchy, and present the explicit
constructions for exact analytical/numerical computations (fast convergent
variational-wavelet representation). Numerical modeling shows the creation of
different internal structures from localized modes, which are related to the
localized (meta) stable patterns (waveletons), entangled ensembles (with
subsequent decoherence) and/or chaotic-like type of behaviour.Comment: LaTeX2e, spie.cls, 13 pages, 6 figures, submitted to Proc. of SPIE
Meeting, The Nature of Light: What is a Photon? Optics & Photonics, SP200,
San Diego, CA, July-August, 200
Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty
We study non-Hermitian quantum mechanics in the presence of a minimal length.
In particular we obtain exact solutions of a non-Hermitian displaced harmonic
oscillator and the Swanson model with minimal length uncertainty. The spectrum
in both the cases are found to be real. It is also shown that the models are
pseudo-Hermitian and the metric operator is found explicitly in both the
cases
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