Using the nonlinear differential equations governing the motion of a fluid-filled and prestressed long thin elastic tube, the propagation of nonlinear waves near the marginal state is examined through the use of reductive perturbation method. It is shown that the amplitude modulation near the marginal state is governed by a generalized nonlinear Schr€ odinger (GNLS) equation. Some exact solutio...

The purpose of this note is to give a combinatorial proof of the three-term linear recurrence for Motzkin numbers. The present work is inspired by R emy’s combinatorial proof of the linear recurrence for Catalan numbers (RAIRO Inform. Theor. 19(2) (1985) 179) and the more recent proof given by Foata and Zeilberger (J. Combin. Theory Ser. A 80(2) (1997) 380) for Schr; oder numbers (Z. Math. Phys...

An adiabatic approach is used to derive a new law for self-focusing in the nonlinear Schr odinger equation that is valid from the early stages of self-focusing until the blowup point. The adiabatic law leads to an analytical formula for the location of the blowup point and can be used to estimate the effects of various small perturbations on self-focusing. The results of the analysis are confir...

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...

The ared horn is modeled according to Webster's equation. A change of variables transforms the equation into the form of the one dimensional Schrodinger wave equation. The Schrodinger form facilitates speci cation of arbitrary axisymmetric wavefronts for the acoustic disturbance within the horn. To provide a physically motivated choice of wavefront shape, Poisson's equation is solved inside t...

Increasing rates of inflammatory bowel disease (IBD) are now seen in populations where it was once uncommon. The pattern of IBD in children of Middle Eastern descent in Australia has never been reported. This study aimed to investigate the burden of IBD in children of Middle Eastern descent at the Sydney Children's Hospital, Randwick (SCHR). The SCHR IBD database was used to identify patients o...