We present the first numerical QCD bound state calculation based on a renormalization group-improved light-front Hamiltonian formalism. The QCD Hamiltonian is determined to second order in the coupling, and it includes two-body confining interactions. We make a momentum expansion, obtaining an equal-time-like Schr˝ odinger equation. This is solved for quark-antiquark constituent states, and we ...

In this paper the time decay rates for the solutions to the Schr odinger–Poisson system in the repulsive case are improved in the context of semiconductor theory. Upper and lower estimates are obtained by using a norm involving the potential energy and the dispersion equation. In the attractive case some examples, based on the Galilean invariance, are proposed showing that the solutions does no...

We predict the possibility of strongly inelastic soliton collisions in a weakly discrete medium from the analysis of twosoliton solution to the nonlinear Schr . odinger equation and confirm the prediction numerically. The effect turns out to be qualitatively independent on the particular type of perturbation. The conditions of mutual trapping of the colliding solitons are discussed as well. r 2...

Let u(x; t) be the solution to the free time-dependent Schrr odinger equation at the point (x; t) in space-time R n+1 with initial data f. We characterize the size of u in terms L p (L q)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces _ H s (R n). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interpo...

In particular, there have been studies within Supersymmetric Quantum Mechanics formalism. Cooper et al, [6], for instance, investigated the relationship between shape invariance and exactly analytical solvable potentials and showed that the Natanzon potential is not shape invariant although it has analytical solutions for the associated Schr odinger equation. L evai et al, [7], have determined...

We present a new system of modulation equations that approximate the focusing of the nonlinear Schrodinger equation in the presence of small normal time dispersion (TDNLS). Since the modulation equations are much easier for analysis and for numerical simulations, they can be used to get a general picture of the TDNLS focusing. Analytical and numerical agreement between the modulation equations...

An eecient numerical algorithm is developed for determining the potential of a conservative system described by a Klein{Gordon or Schrr odinger equation from its normal mode spectra. The algorithm is based on rst solving the linear problem of perturbative inversion by means of Tikhonov regularization, and then using a series of perturbative steps to approach the full potential by Newton's metho...

The possibility of physically relevant singular solutions of the nonlinear Schrr odinger equation (NLSE) with sustained dissipation into the singularity is considered through numerical study of a dissipative regularisation and its small dissipation limit. A new form of such dissipative solutions is conjectured for certain parameter ranges where this behaviour was previously not expected, involv...

The nonlinear coupling of two scalar nonlinear Schrr odinger (NLS) elds results in non-focusing instabilities that exist independently of the well-known modulational instability of the focusing NLS equation. The focusing versus defocusing behavior of scalar NLS elds is a well-known model for the corresponding behavior of pulse transmission in optical bers in the anomalous (focusing) versus norm...

In this article, dissipative perturbations of the nonlinear Schrr odinger equation (NLS) are considered. For dissipative equations, when determining the stability of a solitary wave, one must locate both the point spectrum and the continuous spectrum. If the wave is to be stable, all the spectrum must reside in the left-half plane, except for the translational eigenvalue(s) at the origin. Howev...