390 research outputs found
Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation
The generalized Kuramoto-Sivashinsky equation in the case of the power
nonlinearity with arbitrary degree is considered. New exact solutions of this
equation are presented
On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation
The Conte-Musette method has been modified for the search of only elliptic
solutions to systems of differential equations. A key idea of this a priory
restriction is to simplify calculations by means of the use of a few Laurent
series solutions instead of one and the use of the residue theorem. The
application of our approach to the quintic complex one-dimensional
Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave
form. We also find restrictions on coefficients, which are necessary conditions
for the existence of elliptic solutions for the CGLE5. Using the investigation
of the CGLE5 as an example, we demonstrate that to find elliptic solutions the
analysis of a system of differential equations is more preferable than the
analysis of the equivalent single differential equation.Comment: LaTeX, 21 page
Using a Laguerre-Gaussian beam to trap and cool the rotational motion of a mirror
We show theoretically that it is possible to trap and cool the rotational
motion of a macroscopic mirror made of a perfectly reflecting spiral phase
element using orbital angular momentum transfer from a Laguerre-Gaussian
optical field. This technique offers a promising route to the placement of the
rotor in its quantum mechanical ground state in the presence of thermal noise.
It also opens up the possibility of simultaneously cooling a vibrational mode
of the same mirror. Lastly, the proposed design may serve as a sensitive
torsional balance in the quantum regime.Comment: New cavity design, reworked title; to appear in Phys. Rev. Let
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