Non-interacting gravity waves on the surface of a deep fluid

We study the interaction of gravity waves on the surface of an infinitely deep ideal fluid. Starting from Zakharov's variational formulation for water waves we derive an expansion of the Hamiltonian to an arbitrary order, in a manner that avoids a laborious series reversion associated with expressing the velocity potential in terms of its value at the free surface. The expansion kernels are shown to satisfy a recursion relation enabling us to draw some conclusions about higher-order wave-wave interaction amplitudes, without referring to the explicit forms of the individual lower-order kernels. In particular, we show that unidirectional waves propagating in a two-dimensional flow do not interact nonlinearly provided they fulfill the energy-momentum conservation law. Switching from the physical variables to the so-called normal variables we explain the vanishing of the amplitudes of fourth- and certain fifth-order non-generic resonant interactions reported earlier and outline a procedure for finding the one-dimensional wave vector configurations for which the higher order interaction amplitudes become zero on the resonant hypersurfaces.Comment: 13 page

Zeta-function approach to Casimir energy with singular potentials

In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which are peculiar to the potentials. It is suggested to renormalize the energy using the condition that the energy of infinitely separated potentials is zero which corresponds to subtraction all terms of asymptotic expansion of zeta-function. The energy obtained in this way obeys all physically reasonable conditions. It is finite in the Dirichlet limit and it may be attractive or repulsive depending on the strength of potential. The effective action is calculated and it is shown that the surface contribution appears. The renormalization of the effective action is discussed.Comment: 17 pages, 2 figures, added reference, address correcte

Isospectral Potentials from Modified Factorization

Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.Comment: 8 pages, 4 figure

Few-cycle optical solitary waves in nonlinear dispersive media

We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons

Seroprevalence of Hepatitis B and C among health care workers in Omdurman, Sudan

Background: Health care workers in developing countries including Sudan are at serious risk of infection from blood-borne pathogens particularly HBV and HCV, because of high prevalence of such pathogens in these countries. Methods: A cross sectional study was conducted during November 2007 to determine the seroprevalence of hepatitis B virus ( HBV ) and C ( HCV ) and their associated risk factors among the health care workers ( HCW ) of an urban referral hospital in central Sudan . Enzyme Linked Immunosorbent Assay technique was used to test the blood samples and a questionnaire to collect socio - demographic data of the study participants ( n = 211 ) . Results: The seroprevalence of HBsAg was 2.4%. None of the study participants had HCV antibodies in their blood samples. Age and past history of jaundice were significantly associated with HBsAg infection. The categories of HCW with higher risk of occupational transmission for HBsAg were nurses and non professional staff. Conclusion: The occupation risk of HBV infection among the HCW in this study was high for the nurses and cleaning staff. Effective prevention of HBV infection is mainly by vaccination to unexposed HCW, however acceptance of vaccine should be promoted for such high risk categories. Keywords: Hepatitis B&C; Health care workers; Sudan.Sudan Journal of Medical Sciences Vol. 3 (3) 2008: pp. 201-20

Experimental evidence for soliton explosions

We show, experimentally and numerically, that Ti:sapphire mode-locked lasers can operate in a regime in which they intermittently produce exploding solitons. This happens when the laser operates near a critical point. Explosions happen spontaneously, but external perturbations can trigger them. In stable operation, all explosions have similar features, but are not identical. The characteristics of the explosions depend on the intracavity dispersion

Sasa-Satsuma hierarchy of integrable evolution equations

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms. Up to sixth-order terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higher-order terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly.The authors gratefully acknowledge the support of the Australian Research Council (Discovery Projects DP140100265 and DP150102057) and support from the Volkswagen Stiftung. N.A. is a recipient of the Alexander von Humboldt Award. U.B. acknowledges support by the German Research Foundation in the framework of the Collaborative Research Center 787 “Semiconductor Nanophotonics” under project B5. Sh.A. acknowledges support of the German Research Foundation under Project No. 389251150