Using the symmetries of the three-dimensional Paul trap, we derive the solutions of the time-dependent Schrodinger equation for this system, in both Cartesian and cylindrical coordinates. Our symmetry calculations provide insights that are not always obvious from the conventional viewpoint.

The Schr?dinger differential equation is what we usually solve for the microscopic particles in non-relativistic quantum mechanics. Niels Bohr suggested power two of (usually) complex answer shows probability particle’s existence at a point space. Also, time dependence Schrodinger wave one whereas light electromagnetism two. In this paper, show solution both problems. We derive Wave Equation en...

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlin...

In this paper we consider the solution of the enhanced Boussinesq equations of Madsen and Sørensen (Coast.Eng. 18, 1992) by means of residual based discretizations. In particular, we investigate the applicability of upwind and stabilized variants of the Residual Distribution and Galerkin finite element schemes for the simulation of wave propagation and transformation over complex bathymetries. ...

settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control Mehdi Badra To cite this version: Mehdi Badra. Abstract settings for stabilization of nonlinear parabolic system with a Riccatibased strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichle...

  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...

Minimal length in non-commutative space of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions momentum space. The eigensolutions are found system mapping to well-known Schrodinger equation Pöschl-Teller potential.

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

This paper presents a parametric finite-difference scheme concerning the numerical solution of theone-dimensional Boussinesq-type set of equations, as they were introduced byPeregrine, in the case of wavesrelatively long with small amplitudes in water of constant depth. The method which is used can be considered asa generalization of the Crank-Nickolson method and it has been ap...