Interactions of breathers and solitons in the extended Korteweg-de Vries equation

The extended Korteweg-de Vries model governs the evolution of weakly dispersive waves under the combined influence of quadratic and cubic nonlinearities, and is relevant to finite-amplitude wave motions in the atmosphere and the ocean. Analytic expressions for a multi-soliton are obtained by the Hirota bilinear method, and are shown to agree with those for isolated solitary waves or breathers obtained earlier in the literature. In particular, the interaction of a breather and a soliton can now be studied. Both the soliton and the breather retain their identities after interaction except for some phase shifts. Detailed examination of the interaction process shows that the profile of the breather will depend critically on the polarity of the colliding soliton. © 2005 Elsevier B.V. All rights reserved.postprin

Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation

Generation of mode 2 internal waves by the interaction of mode 1 waves with topography

Oceanic internal waves can be decomposed into an infinite set of modes, and the dominant internal mode 1 waves have been extensively investigated. Although mode 2 waves have been observed, they have not received comparable attention, especially the generation mechanisms. In this work, we examine the generation of mode 2 internal waves by the interaction of mode 1 waves with topography. We use a coupled linear long-wave theory with mode coupling through topography, combined with evolution using a Korteweg–de Vries model, to predict the mode 2 wave amplitude, in an ideal three-layer fluid model, in a smooth density stratification and in two realistic oceanic settings. We find that the mode 2 wave amplitude is usually much smaller than the incident mode 1 wave amplitude and is quite sensitive to the pycnocline thickness, topographic slope and background stratification

Genotype moderates the impact of food additives on hyperactive behavior in children

Introduction: The claim of a relationship between artificial food color and additive (AFCs) intake and behavior is highly contentious. We have shown in a previous population-based trial with 3yo children adverse effects of food additives on parentally-rated hyperactive behaviour (Bateman et al, 2004). The possible role of genetic polymorphisms in moderating this adverse effect has not been previously examined. Methods A randomised, double blind, placebo-controlled, within subject crossover food challenge was used for 144, 8 to 9 year old children and 153, 3 year old children. Following baseline assessment children were placed on a diet eliminating food additives and a benzoate preservative for 6 weeks during which time they were challenged for weekly periods with either a placebo mix or a drink containing sodium benzoate (45mg daily) and one of two mixes of AFCs.: Results: The T939C and Thr105Ile polymorphisms of the histamine N-methyltransferase gene (HNMT) moderated the adverse effect s of AFCs but the polymorphisms in catecholamine genes COMT Val108Met and ADRA2A C1291G did not. These findings point to a possible role for histamine in mediating the effects of food additives and help to explain why there has been inconsistency between previous studies. Conclusions: Genes influencing a range of neurotransmitter systems and their interplay with environmental factors, such as diet, need to be examined to understand genetic influences on hyperactivity.<br/

Stable embedded solitons

Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum.Comment: 2 figures. To appear in Phys. Rev. Let

Interactions of breathers and solitons of the extended Korteweg - de Vries equation

Session HL: Waves II, Abstract no. HL.00002published_or_final_versio

A systematic review of the use of theory in the design of guideline dissemination and implementation strategies and interpretation of the results of rigorous evaluations

<p>Abstract</p> <p>Background</p> <p>There is growing interest in the use of cognitive, behavioural, and organisational theories in implementation research. However, the extent of use of theory in implementation research is uncertain.</p> <p>Methods</p> <p>We conducted a systematic review of use of theory in 235 rigorous evaluations of guideline dissemination and implementation studies published between 1966 and 1998. Use of theory was classified according to type of use (explicitly theory based, some conceptual basis, and theoretical construct used) and stage of use (choice/design of intervention, process/mediators/moderators, and post hoc/explanation).</p> <p>Results</p> <p>Fifty-three of 235 studies (22.5%) were judged to have employed theories, including 14 studies that explicitly used theory. The majority of studies (n = 42) used only one theory; the maximum number of theories employed by any study was three. Twenty-five different theories were used. A small number of theories accounted for the majority of theory use including PRECEDE (Predisposing, Reinforcing, and Enabling Constructs in Educational Diagnosis and Evaluation), diffusion of innovations, information overload and social marketing (academic detailing).</p> <p>Conclusions</p> <p>There was poor justification of choice of intervention and use of theory in implementation research in the identified studies until at least 1998. Future research should explicitly identify the justification for the interventions. Greater use of explicit theory to understand barriers, design interventions, and explore mediating pathways and moderators is needed to advance the science of implementation research.</p

Generation of nonlinear internal waves by flow over topography: Rotational effects

We use the forced Ostrovsky equation to investigate the generation of internal waves excited by a constant background current flowing over localized topography in the presence of background rotation. As is now well known in the absence of background rotation, the evolution scenarios fall into three cases, namely subcritical, transcritical, and supercritical. Here an analysis of the linearized response divides the waves into steady and unsteady waves. In all three cases, steady waves occur downstream but no steady waves can occur upstream, while unsteady waves can arise upstream only when there is a negative minimum of the group velocity. The regions occupied by the steady and unsteady waves are determined by their respective group velocities. When the background current is increased, the wave number of the steady waves decreases. In addition, the concavity (canyon or sill), the topographic width, and the relative strength of the rotation play an important role in the generation mechanism. Nonlinear effects modulate the wave amplitude and lead to the emergence of coherent wave packets. All these findings are confirmed by numerical simulations

Using the theory of planned behaviour as a process evaluation tool in randomised trials of knowledge translation strategies : A case study from UK primary care

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