Stability of Compacton Solutions of Fifth-Order Nonlinear Dispersive Equations

We consider fifth-order nonlinear dispersive $K(m,n,p)$ type equations to study the effect of nonlinear dispersion. Using simple scaling arguments we show, how, instead of the conventional solitary waves like solitons, the interaction of the nonlinear dispersion with nonlinear convection generates compactons - the compact solitary waves free of exponential tails. This interaction also generates many other solitary wave structures like cuspons, peakons, tipons etc. which are otherwise unattainable with linear dispersion. Various self similar solutions of these higher order nonlinear dispersive equations are also obtained using similarity transformations. Further, it is shown that, like the third-order nonlinear $K(m,n)$ equations, the fifth-order nonlinear dispersive equations also have the same four conserved quantities and further even any arbitrary odd order nonlinear dispersive $K(m,n,p...)$ type equations also have the same three (and most likely the four) conserved quantities. Finally, the stability of the compacton solutions for the fifth-order nonlinear dispersive equations are studied using linear stability analysis. From the results of the linear stability analysis it follows that, unlike solitons, all the allowed compacton solutions are stable, since the stability conditions are satisfied for arbitrary values of the nonlinear parameters.Comment: 20 pages, To Appear in J.Phys.A (2000), several modification

Standard noncommuting and commuting dilations of commuting tuples

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly there is the minimal isometric dilation consisting of isometries with orthogonal ranges and hence it is a noncommuting tuple. There is also a commuting dilation related with a standard commuting tuple on Boson Fock space. We show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation. We use this result to classify all representations of Cuntz algebra O_n coming from dilations of commuting tuples.Comment: 18 pages, Latex, 1 commuting diagra

S3S_3 symmetry and the quark mixing matrix

We impose an $S_3$ symmetry on the quark fields under which two of three quarks transform like a doublet and the remaining one as singlet, and use a scalar sector with the same structure of $SU(2)$ doublets. After gauge symmetry breaking, a $\mathbb{Z}_2$ subgroup of the $S_3$ remains unbroken. We show that this unbroken subgroup can explain the approximate block structure of the CKM matrix. By allowing soft breaking of the $S_3$ symmetry in the scalar sector, we show that one can generate the small elements, of quadratic or higher order in the Wolfenstein parametrization of the CKM matrix. We also predict the existence of exotic new scalars, with unconventional decay properties, which can be used to test our model experimentally.Comment: 7 pages, no figur

Orbital Sensing of Mackenzie Bay Ice Dynamics

Satellite images are a useful tool in the study of sea ice dynamics. The results of studies using satellite images of Mackenzie Bay during the break-up and freeze-up periods are presented in maps and tables. These indicate important temporal variations in the processes of bay ice break-up and freeze-up. Though the Mackenzie Bay break-up proceeds from the south and from the north, the southern melt rate is faster because of an influx of warm water from the Mackenzie River. The freeze-up proceeds from south to north, i.e., from the fresh water area to the saline water area of the bay. The study of Mackenzie Bay ice dynamics is important because of the barge traffic through the Mackenzie River and also because of offshore drilling activities in the Beaufort Sea