35,787 research outputs found
Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations
Flows on the moduli space of the algebraic Riemann surfaces, preserving the
periods of the corresponding solutions of the soliton equations are studied. We
show that these flows are gradient with respect to some indefinite symmetric
flat metric arising in the Hamiltonian theory of the Whitham equations. The
functions generating these flows are conserved quantities for all the equations
simultaneously. We show that for 1+1 systems these flows can be imbedded in a
larger system of ordinary nonlinear differential equations with a rational
right-hand side. Finally these flows are used to give a complete description of
the moduli space of algebraic Riemann surfaces corresponding to periodic
solutions of the nonlinear Schr\"odinger equation.Comment: 35 pages, LaTex. Macros file elsart.sty is used (it was submitted by
the authors to [email protected] library macroses),e-mail:
[email protected], e-mail:[email protected]
Closed curves in R^3: a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the Filament Equation
If a curve in R^3 is closed, then the curvature and the torsion are periodic
functions satisfying some additional constraints. We show that these
constraints can be naturally formulated in terms of the spectral problem for a
2x2 matrix differential operator. This operator arose in the theory of the
self-focusing Nonlinear Schrodinger Equation.
A simple spectral characterization of Bloch varieties generating periodic
solutions of the Filament Equation is obtained. We show that the method of
isoperiodic deformations suggested earlier by the authors for constructing
periodic solutions of soliton equations can be naturally applied to the
Filament Equation.Comment: LaTeX, 27 pages, macros "amssym.def" use
Infinite Infrared Regularization and a State Space for the Heisenberg Algebra
We present a method for the construction of a Krein space completion for
spaces of test functions, equipped with an indefinite inner product induced by
a kernel which is more singular than a distribution of finite order. This
generalizes a regularization method for infrared singularities in quantum field
theory, introduced by G. Morchio and F. Strocchi, to the case of singularites
of infinite order. We give conditions for the possibility of this procedure in
terms of local differential operators and the Gelfand- Shilov test function
spaces, as well as an abstract sufficient condition. As a model case we
construct a maximally positive definite state space for the Heisenberg algebra
in the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde
Structural investigations on -FeGe at high pressure and low temperature
The structural parameters of -FeGe have been determined at ambient
conditions using single crystal refinement. Powder diffraction have been
carried out to determine structural properties and compressibility for
pressures up to 30 GPa and temperatures as low as 82 K. The discontinuous
change in the pressure dependence of the shortest Fe-Ge interatomic distance
might be interpreted as a symmetry-conserving transition and seems to be
related to a magnetic phase boundary line.Comment: 4 pages, 5 figure
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