The evolution of free wave packets
نویسنده
چکیده
We discuss four general features of the force-free evolution of wave packets: 1 The spatial spread of a packet changes with time in a simple way. 2 For sufficiently short durations related to the spread in the momentum of the packet the probability distribution will move with uniform speed and little change in shape. 3 After a sufficiently long time related to the initial spatial spread the wave function converges to a simple form that is simply related to the momentum distribution of the packet. In this asymptotic regime the shape of the probability distribution no longer changes, and its scale increases linearly with the time. 4 There is an infinite denumerable set of simple wave packets the Hermite-Gauss packets that do not change shape at any time during their evolution. ©
منابع مشابه
STABILITY ANALYSIS FROM FOURTH ORDER NONLINEAR EVOLUTION EQUATIONS FOR TWO CAPILLARY GRAVITY WAVE PACKETS IN THE PRESENCE OF WIND OWING OVER WATER.
Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution eq...
متن کاملEFFECT OF COUNTERPROPAGATING CAPILLARY GRAVITY WAVE PACKETS ON THIRD ORDER NONLINEAR EVOLUTION EQUATIONS IN THE PRESENCE OF WIND FLOWING OVER WATER
Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and g...
متن کاملCharge gradient effects on modulated dust lattice wave packets in dusty plasma crystals
Nonlinear Dust lattice modes are studied in a hexagonal two-dimensional dusty plasma lattice, in presence of charge gradient of dust particles. In this lattice, such gradients affect nonlinear behavior of dust lattice waves. The amplitude modulation of off-plane transverse dust lattice wave packets is investigated considering the anisotropy of interactions, caused by the height-dependent char...
متن کاملWave Evolution in Water Bodies using Turbulent MPS Simulation
Moving Particle Semi-implicit (MPS) which is a meshless and full Lagrangian method is employed to simulate nonlinear hydrodynamic behavior in a wide variety of engineering application including free surface water waves. In the present study, a numerical particle-based model is developed by the authors using MPS method to simulate different wave problems in the coastal waters. In this model flui...
متن کاملInstabilities of Thin Viscous Liquid Film Flowing down a Uniformly Heated Inclined Plane
Instabilities of a thin viscous film flowing down a uniformly heated plane are investigated in this study. The heating generates a surface tension gradient that induces thermocapillary stresses on the free surface. Thus, the film is not only influenced by gravity and mean surface tension but also the thermocapillary force is acting on the free surface. Moreover, the heat transfer at the free su...
متن کامل