232 research outputs found
Variational derivation of two-component Camassa-Holm shallow water system
By a variational approach in the Lagrangian formalism, we derive the
nonlinear integrable two-component Camassa-Holm system (1). We show that the
two-component Camassa-Holm system (1) with the plus sign arises as an
approximation to the Euler equations of hydrodynamics for propagation of
irrotational shallow water waves over a flat bed. The Lagrangian used in the
variational derivation is not a metric.Comment: to appear in Appl. Ana
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
Two-component Analogue of Two-dimensional Long Wave-Short Wave Resonance Interaction Equations: A Derivation and Solutions
The two-component analogue of two-dimensional long wave-short wave resonance
interaction equations is derived in a physical setting. Wronskian solutions of
the integrable two-component analogue of two-dimensional long wave-short wave
resonance interaction equations are presented.Comment: 16 pages, 9 figures, revised version; The pdf file including all
figures: http://www.math.utpa.edu/kmaruno/yajima.pd
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
Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures
Results of numerical simulations of a recently derived most general
dissipative-dispersive PDE describing evolution of a film flowing down an
inclined plane are presented. They indicate that a novel complex type of
spatiotemporal patterns can exist for strange attractors of nonequilibrium
systems. It is suggested that real-life experiments satisfying the validity
conditions of the theory are possible: the required sufficiently viscous
liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations
available upon or reques
Vlasov moment flows and geodesics on the Jacobi group
By using the moment algebra of the Vlasov kinetic equation, we characterize
the integrable Bloch-Iserles system on symmetric matrices
(arXiv:math-ph/0512093) as a geodesic flow on the Jacobi group. We analyze the
corresponding Lie-Poisson structure by presenting a momentum map, which both
untangles the bracket structure and produces particle-type solutions that are
inherited from the Vlasov-like interpretation. Moreover, we show how the Vlasov
moments associated to Bloch-Iserles dynamics correspond to particular subgroup
inclusions into a group central extension (first discovered in
arXiv:math/0410100), which in turn underlies Vlasov kinetic theory. In the most
general case of Bloch-Iserles dynamics, a generalization of the Jacobi group
also emerges naturally.Comment: 45 page
Evolution of Rogue Waves in Interacting Wave Systems
Large amplitude water waves on deep water has long been known in the sea
faring community, and the cause of great concern for, e.g., oil platform
constructions. The concept of such freak waves is nowadays, thanks to satellite
and radar measurements, well established within the scientific community. There
are a number of important models and approaches for the theoretical description
of such waves. By analyzing the scaling behavior of freak wave formation in a
model of two interacting waves, described by two coupled nonlinear Schroedinger
equations, we show that there are two different dynamical scaling behaviors
above and below a critical angle theta_c of the direction of the interacting
waves below theta_c all wave systems evolve and display statistics similar to a
wave system of non-interacting waves. The results equally apply to other
systems described by the nonlinear Schroedinger equations, and should be of
interest when designing optical wave guides.Comment: 5 pages, 2 figures, to appear in Europhysics Letter
Asymptotic solution for the two-body problem with constant tangencial acceleration
An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error
Singular sectors of the 1-layer Benney and dToda systems and their interrelations
Complete description of the singular sectors of the 1-layer Benney system
(classical long wave equation) and dToda system is presented. Associated
Euler-Poisson-Darboux equations E(1/2,1/2) and E(-1/2,-1/2) are the main tool
in the analysis. A complete list of solutions of the 1-layer Benney system
depending on two parameters and belonging to the singular sector is given.
Relation between Euler-Poisson-Darboux equations E(a,a) with opposite sign of a
is discussed.Comment: 15 pages; Theor. Mathem. Physics, 201
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