331 research outputs found
On the Quantum Kinetic Equation in Weak Turbulence
The quantum kinetic equation used in the study of weak turbulence is
reconsidered in the context of a theory with a generic quartic interaction. The
expectation value of the time derivative of the mode number operators is
computed in a perturbation expansion which places the large diagonal component
of the quartic term in the unperturbed Hamiltonian. Although one is not
perturbing around a free field theory, the calculation is easily tractable
owing to the fact that the unperturbed Hamiltonian can be written solely in
terms of the mode number operators.Comment: 12 pages, LATEX, no figures, to appear in Phys. Rev.
On the analytical approach to the N-fold B\"acklund transformation of Davey-Stewartson equation
N-fold B\"acklund transformation for the Davey-Stewartson equation is
constructed by using the analytic structure of the Lax eigenfunction in the
complex eigenvalue plane. Explicit formulae can be obtained for a specified
value of N. Lastly it is shown how generalized soliton solutions are generated
from the trivial ones
Variational principle for frozen-in vortex structures interacting with sound waves
General properties of conservative hydrodynamic-type models are treated from
positions of the canonical formalism adopted for liquid continuous media, with
applications to the compressible Eulerian hydrodynamics, special- and
general-relativistic fluid dynamics, and two-fluid plasma model including the
Hall-magnetohydrodynamics. A variational formulation is found for motion and
interaction of frozen-in localized vortex structures and acoustic waves in a
special description where dynamical variables are, besides the Eulerian fields
of the fluid density and the potential component of the canonical momentum,
also the shapes of frozen-in lines of the generalized vorticity. This
variational principle can serve as a basis for approximate dynamical models
with reduced number of degrees of freedom.Comment: 7 pages, revtex4, no figure
A constructive approach to the soliton solutions of integrable quadrilateral lattice equations
Scalar multidimensionally consistent quadrilateral lattice equations are
studied. We explore a confluence between the superposition principle for
solutions related by the Backlund transformation, and the method of solving a
Riccati map by exploiting two kn own particular solutions. This leads to an
expression for the N-soliton-type solutions of a generic equation within this
class. As a particular instance we give an explicit N-soliton solution for the
primary model, which is Adler's lattice equation (or Q4).Comment: 22 page
On the asymptotic expansion of the solutions of the separated nonlinear Schroedinger equation
Nonlinear Schr\"odinger equation (with the Schwarzian initial data) is
important in nonlinear optics, Bose condensation and in the theory of strongly
correlated electrons. The asymptotic solutions in the region ,
, can be represented as a double series in and .
Our current purpose is the description of the asymptotics of the coefficients
of the series.Comment: 11 pages, LaTe
On domination of nonlinear wave interaction in the energy balance of wind-driven sea
Here some aspects of the physics of wind-driven sea are investigated theoretically. It is demonstrated that the effective four-wave nonlinear interaction plays the leading role in the formation of the spectra of turbulent waves. In particular this interaction leads to non-linear damping which exceeds standard data at least by the order of magnitude. The theory developed here is compared with the available experimental data
Generic solutions for some integrable lattice equations
We derive the expressions for -functions and generic solutions of
lattice principal chiral equations, lattice KP hierarchy and hierarchy
including lattice N-wave type equations. -function of free fermions
plays fundamental role in this context. Miwa's coordinates in our case appear
as the lattice parameters.Comment: The text of the talk at NEEDS-93 conference, Gallipoli, Italy,
September-93, LaTeX, 8 pages. Several typos and minor errors are correcte
Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions
Several theories for weakly damped free-surface flows have been formulated.
In this paper we use the linear approximation to the Navier-Stokes equations to
derive a new set of equations for potential flow which include dissipation due
to viscosity. A viscous correction is added not only to the irrotational
pressure (Bernoulli's equation), but also to the kinematic boundary condition.
The nonlinear Schr\"odinger (NLS) equation that one can derive from the new set
of equations to describe the modulations of weakly nonlinear, weakly damped
deep-water gravity waves turns out to be the classical damped version of the
NLS equation that has been used by many authors without rigorous justification
Quantum equivalence in Poisson-Lie T-duality
We prove that, general \s-models related by Poisson-Lie T-duality are
quantum equivalent under one-loop renormalization group flow. We reveal general
properties of the flows, we study the associated generalized coset models and
provide explicit examples.Comment: 16 page
Numerical Verification of the Weak Turbulent Model for Swell Evolution
The purpose of this article is numerical verification of the theory of weak
turbulence. We performed numerical simulation of an ensemble of nonlinearly
interacting free gravity waves (swell) by two different methods: solution of
primordial dynamical equations describing potential flow of the ideal fluid
with a free surface and, solution of the kinetic Hasselmann equation,
describing the wave ensemble in the framework of the theory of weak turbulence.
In both cases we observed effects predicted by this theory: frequency
downshift, angular spreading and formation of Zakharov-Filonenko spectrum
. To achieve quantitative coincidence of the
results obtained by different methods, one has to supply the Hasselmann kinetic
equation by an empirical dissipation term modeling the coherent
effects of white-capping. Using of the standard dissipation terms from
operational wave predicting model ({\it WAM}) leads to significant improvement
on short times, but not resolve the discrepancy completely, leaving the
question about optimal choice of open. In a long run {\it WAM}
dissipative terms overestimate dissipation essentially.Comment: 41 pages, 37 figures, 1 table. Submitted in European Journal of
Mechanics B/Fluid
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