216 research outputs found
Finite time collapse of N classical fields described by coupled nonlinear Schrodinger equations
We prove the finite-time collapse of a system of N classical fields, which
are described by N coupled nonlinear Schrodinger equations. We derive the
conditions under which all of the fields experiences this finite-time collapse.
Finally, for two-dimensional systems, we derive constraints on the number of
particles associated with each field that are necessary to prevent collapse.Comment: v2: corrected typo on equation
Statistical Description of Acoustic Turbulence
We develop expressions for the nonlinear wave damping and frequency
correction of a field of random, spatially homogeneous, acoustic waves. The
implications for the nature of the equilibrium spectral energy distribution are
discussedComment: PRE, Submitted. REVTeX, 16 pages, 3 figures (not included) PS Source
of the paper with figures avalable at
http://lvov.weizmann.ac.il/onlinelist.htm
A Singular Perturbation Analysis for \\Unstable Systems with Convective Nonlinearity
We use a singular perturbation method to study the interface dynamics of a
non-conserved order parameter (NCOP) system, of the reaction-diffusion type,
for the case where an external bias field or convection is present. We find
that this method, developed by Kawasaki, Yalabik and Gunton for the
time-dependant Ginzburg-Landau equation and used successfully on other NCOP
systems, breaks down for our system when the strength of bias/convection gets
large enough.Comment: 5 pages, PostScript forma
Algebro-geometric approach in the theory of integrable hydrodynamic type systems
The algebro-geometric approach for integrability of semi-Hamiltonian
hydrodynamic type systems is presented. This method is significantly simplified
for so-called symmetric hydrodynamic type systems. Plenty interesting and
physically motivated examples are investigated
Performance, Control, and Simulation of the Affordable Guided Airdrop System
This paper addresses the development of an autonomous
guidance, navigation and control system for a flat
solid circular parachute. This effort is a part of the Affordable
Guided Airdrop System (AGAS) that integrates
a low-cost guidance and control system into
fielded cargo air delivery systems. The paper describes
the AGAS concept, its architecture and components. It
then reviews the literature on circular parachute modeling
and introduces a simplified model of a parachute.
This model is used to develop and evaluate the performance
of a modified bang-bang control system to
steer the AGAS along a pre-specified trajectory towards
a desired landing point. The synthesis of the optimal
control strategy based on Pontryagin's principle of optimality
is also presented. The paper is intended to be a
summary of the current state of AGAS development.
The paper ends with the summary of the future plans in
this area
Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations
In this paper, we consider Hartree-type equations on the two-dimensional
torus and on the plane. We prove polynomial bounds on the growth of high
Sobolev norms of solutions to these equations. The proofs of our results are
based on the adaptation to two dimensions of the techniques we previously used
to study analogous problems on , and on .Comment: 38 page
Energy spectra of the ocean's internal wave field: theory and observations
The high-frequency limit of the Garrett and Munk spectrum of internal waves
in the ocean and the observed deviations from it are shown to form a pattern
consistent with the predictions of wave turbulence theory. In particular, the
high frequency limit of the Garrett and Munk spectrum constitutes an {\it
exact} steady state solution of the corresponding kinetic equation.Comment: 4 pages, one color figur
Instability and Evolution of Nonlinearly Interacting Water Waves
We consider the modulational instability of nonlinearly interacting
two-dimensional waves in deep water, which are described by a pair of
two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear
dispersion relation. The latter is numerically analyzed to obtain the regions
and the associated growth rates of the modulational instability. Furthermore,
we follow the long term evolution of the latter by means of computer
simulations of the governing nonlinear equations and demonstrate the formation
of localized coherent wave envelopes. Our results should be useful for
understanding the formation and nonlinear propagation characteristics of large
amplitude freak waves in deep water.Comment: 4 pages, 4 figures, to appear in Physical Review Letter
Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de Vries equations
Periodic waves are investigated in a system composed of a
Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly
coupled to an extra linear dissipative equation. The model describes, e.g., a
two-layer liquid film flowing down an inclined plane. It has been recently
shown that the system supports stable solitary pulses. We demonstrate that a
perturbation analysis, based on the balance equation for the field momentum,
predicts the existence of stable cnoidal waves (CnWs) in the same system. It is
found that the mean value U of the wave field u in the main subsystem, but not
the mean value of the extra field, affects the stability of the periodic waves.
Three different areas can be distinguished inside the stability region in the
parameter plane (L,U), where L is the wave's period. In these areas, stable
are, respectively, CnWs with positive velocity, constant solutions, and CnWs
with negative velocity. Multistability, i.e., the coexistence of several
attractors, including the waves with several maxima per period, appears at
large value of L. The analytical predictions are completely confirmed by direct
simulations. Stable waves are also found numerically in the limit of vanishing
dispersion, when the KS-KdV equation goes over into the KS one.Comment: a latex text file and 16 eps files with figures. Journal of the
Physical Society of Japan, in pres
KP solitons in shallow water
The main purpose of the paper is to provide a survey of our recent studies on
soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The
classification is based on the far-field patterns of the solutions which
consist of a finite number of line-solitons. Each soliton solution is then
defined by a point of the totally non-negative Grassmann variety which can be
parametrized by a unique derangement of the symmetric group of permutations.
Our study also includes certain numerical stability problems of those soliton
solutions. Numerical simulations of the initial value problems indicate that
certain class of initial waves asymptotically approach to these exact solutions
of the KP equation. We then discuss an application of our theory to the Mach
reflection problem in shallow water. This problem describes the resonant
interaction of solitary waves appearing in the reflection of an obliquely
incident wave onto a vertical wall, and it predicts an extra-ordinary four-fold
amplification of the wave at the wall. There are several numerical studies
confirming the prediction, but all indicate disagreements with the KP theory.
Contrary to those previous numerical studies, we find that the KP theory
actually provides an excellent model to describe the Mach reflection phenomena
when the higher order corrections are included to the quasi-two dimensional
approximation. We also present laboratory experiments of the Mach reflection
recently carried out by Yeh and his colleagues, and show how precisely the KP
theory predicts this wave behavior.Comment: 50 pages, 25 figure
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