We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by correlation function. Given the operator product expansion (OPE) of function in deep Euclidean region, we obtain nonperturbative spectral density, which exhibits structures naturally. The value gluon condensate OPE is fixed producing $\rho$ meson mass formalism, and then input into relations s...

We demonstrate that fermion masses in the Standard Model (SM) can be constrained by dispersion relations obeyed hadronic and semileptonic decay widths of a fictitious heavy quark $Q$ with an arbitrary mass. These relations, imposing stringent connections between high-mass low-mass behaviors widths, correlate mass chiral symmetry breaking scale. Given known input from leading-order expansion thr...

We investigate L → L∞ dispersive estimates for the Schrödinger equation iut − ∆u + V u = 0 in odd dimensions greater than three. We obtain dispersive estimates under the optimal smoothness condition for the potential, V ∈ C(n−3)/2(Rn), in dimensions five and seven. We also describe a method to extend this result to arbitrary odd dimensions.

We show analytically that tailoring the fiber dispersion appropriately can cause optical solitons to propagate unperturbed, without emission of dispersive waves, in a distributed-gain fiber amplifier with a nonuniform gain profile. We apply our scheme to a bidirectionally pumped fiber amplifier and discuss the importance of higher-order nonlinear and dispersive effects for short solitons.

We transpose work by K.Yajima and by T.Mizumachi to prove dispersive and smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schrödinger equation (NLS) in 2D. As an application we extend to dimension 2D a result on asymptotic stability of ground states of NLS proved in the literature for all dimensions different from 2. §

The diffraction of pulsed beams of light is formulated as an anomalously dispersive phenomenon. In a dispersive material, the effects of material group-velocity dispersion and diffraction on pulsed beam propagation can mutually cancel if the transverse profile of the pulse is suitably chosen.

In recent years two nonlinear dispersive partial differential equations have attracted much attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water waves over a flat bed. The equations capture stronger nonlinear effects than the classical nonlinear dispersive Benjamin–Bona–Mahoney and Korteweg–de Vries equations. In par...

Scattering of a dispersive wave by optical solitons is studied experimentally in photonic crystal fibers in cases when the soliton and the dispersive wave have either identical or orthogonal polarization states. Observations of new resonant frequencies are reported. The experimental results are compared to numerical simulations and predictions from the recently derived wave vector matching cond...