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

Broken electroweak phase at high temperature in the Littlest Higgs model with T-parity

We have examined in detail the nonrestoration of symmetry at high temperature in a finite-temperature Littlest Higgs model, without and with T-parity, by evaluating the one-loop-order finite-temperature integrals of the effective potential numerically, without the high-temperature approximation, We observe that in the model without T-parity it is not possible to find a transition temperature within the allowed temperature range of the model (0<T<4f) if the UV completion factors are those which give the Standard Model electroweak minimum, as the effective potential always increases with temperature in the positive direction. However, in the case of the model with T-parity, it is possible to find a transition temperature with the same set of UV completion factors, as, with the increase of temperature, the effective potential decreases in magnitude in the positive side, becomes negative, and increases in magnitude in the negative side, indicating symmetry breaking at high temperature. This type of symmetry nonrestoration at high temperature has been observed earlier in some models involving pseudo Nambu-Goldstone bosons. The behaviour of the global structure of the effective potential with T-parity in the theory indicates a strong first order electroweak phase transition, conducive to baryogenesis in the early universe.Comment: 25 pages, 9 colour figures, references updated, explanation adde

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

A Comparative Note on Tunneling in AdS and in its Boundary Matrix Dual

For charged black hole, within the grand canonical ensemble, the decay rate from thermal AdS to the black hole at a fixed high temperature increases with the chemical potential. We check that this feature is well captured by a phenomenological matrix model expected to describe its strongly coupled dual. This comparison is made by explicitly constructing the kink and bounce solutions around the de-confinement transition and evaluating the matrix model effective potential on the solutions.Comment: 1+12 pages, 9 figure