1,297 research outputs found
Stability of Compacton Solutions of Fifth-Order Nonlinear Dispersive Equations
We consider fifth-order nonlinear dispersive 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 equations, the fifth-order
nonlinear dispersive equations also have the same four conserved quantities and
further even any arbitrary odd order nonlinear dispersive 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
Spontaneous Symmetry Breaking and the Renormalization of the Chern-Simons Term
We calculate the one-loop perturbative correction to the coefficient of the
\cs term in non-abelian gauge theory in the presence of Higgs fields, with a
variety of symmetry-breaking structures. In the case of a residual
symmetry, radiative corrections do not change the coefficient of the \cs term.
In the case of an unbroken non-abelian subgroup, the coefficient of the
relevant \cs term (suitably normalized) attains an integral correction, as
required for consistency of the quantum theory. Interestingly, this coefficient
arises purely from the unbroken non-abelian sector in question; the orthogonal
sector makes no contribution. This implies that the coefficient of the \cs term
is a discontinuous function over the phase diagram of the theory.Comment: Version to be published in Phys Lett B., minor additional change
Truncated Harmonic Osillator and Parasupersymmetric Quantum Mechanics
We discuss in detail the parasupersymmetric quantum mechanics of arbitrary
order where the parasupersymmetry is between the normal bosons and those
corresponding to the truncated harmonic oscillator. We show that even though
the parasusy algebra is different from that of the usual parasusy quantum
mechanics, still the consequences of the two are identical. We further show
that the parasupersymmetric quantum mechanics of arbitrary order p can also be
rewritten in terms of p supercharges (i.e. all of which obey ).
However, the Hamiltonian cannot be expressed in a simple form in terms of the p
supercharges except in a special case. A model of conformal parasupersymmetry
is also discussed and it is shown that in this case, the p supercharges, the p
conformal supercharges along with Hamiltonian H, conformal generator K and
dilatation generator D form a closed algebra.Comment: 9 page
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