Volume 46, Issue 3
March 1996, pages 161-243
pp 161-202 March 1996 Review
Coupled scalar field equations for nonlinear wave modulations in dispersive media
A review of the generic features as well as the exact analytical solutions of a class of coupled scalar field equations governing nonlinear wave modulations in dispersive media like plasmas is presented. The equations are derivable from a Hamiltonian function which, in most cases, has the unusual property that the associated kinetic energy is not positive definite. To start with, a simplified derivation of the nonlinear Schrödinger equation for the coupling of an amplitude modulated high-frequency wave to a suitable low-frequency wave is discussed. Coupled sets of time-evolution equations like the Zakharov system, the Schrödinger-Boussinesq system and the Schrödinger-Korteweg-de Vries system are then introduced. For stationary propagation of the coupled waves, the latter two systems yield a generic system of a pair of coupled, ordinary differential equations with many free parameters. Different classes of exact analytical solutions of the generic system of equations are then reviewed. A comparison between the various sets of governing equations as well as between their exact analytical solutions is presented. Parameter regimes for the existence of different types of localized solutions are also discussed. The generic system of equations has a Hamiltonian structure, and is closely related to the well-known Hénon-Heiles system which has been extensively studied in the field of nonlinear dynamics. In fact, the associated generic Hamiltonian is identically the same as the generalized Hénon-Heiles Hamiltonian for the case of coupled waves in a magnetized plasma with negative group dispersion. When the group dispersion is positive, there exists a novel Hamiltonian which is structurally same as the generalized Hénon-Heiles Hamiltonian but with indefinite kinetic energy. The above correspondence between the two systems has been exploited to obtain the parameter regimes for the complete integrability of the coupled waves. There exists a direct one-to-one correspondence between the known integrable cases of the generic Hamiltonian and the stationary Hamiltonian flows associated with the only integrable nonlinear evolution equations (of polynomial and autonomous type) with a scale-weight of seven. The relevance of the generic system to other equations like the self-dual Yang-Mills equations, the complex Korteweg-de Vries equation and the complexified classical dynamical equations has also been discussed.
pp 203-211 March 1996 Research Articles
Self-interacting one-dimensional oscillators
Energy eigenvalues and 〈x^{2}〉_{n} for the oscillators having potential energyV(x)=(ω^{2}x^{2}/2)+λ<x^{2r}>x^{2s} have been determined for various values ofλ, r, s andn using renormalized hypervirial-Padé scheme. In general, the results show an improvement over the findings of earlier workers. Variation of the evaluated quantities and of the renormalization parameter withλ, r, s andn has been discussed. In addition, this potential has been employed as an illustrative example of the applicability of alternative formalism of perturbation theory developed by Kim and Sukhatme (J. Phys.A25 647 (1992)).
pp 213-217 March 1996 Research Articles
The full version of the causal thermodynamics of non-equilibrium phenomena is discussed in the context of the flat Friedmann-Robertson-Walker cosmological model. Power law solutions for the scale factor are shown to exist. It is also shown that the temporal behaviour of the temperature depends on the functional dependence of the coefficient of bulk viscosity on density.
pp 219-221 March 1996 Research Articles
An identity for 4-spacetimes embedded intoE_{5}
José L López-Bonilla H N Núñez-Yépez
We show that if a 4-spacetimeV_{4} can be embedded intoE_{5} then, ifb_{ij}is the second fundamental form tensor associated withV_{4}, the quantity (traceb)·b_{ij}^{/−1} depends only on intrinsic geometric properties of the spacetime. Such fact is used to obtain a necessary condition for the embedding of aV_{4} intoE_{5}.
pp 223-227 March 1996 Research Articles
Aq deformation of Gell-Mann-Okubo mass formula
We explore the possibility of deforming Gell-Mann-Okubo (GMO) mass formula within the framework of a quantized enveloping algebra. A small value of the deformation parameter is found to provide a good fit to the observed mass spectra of theπ, K andη mesons.
pp 229-237 March 1996 Research Articles
Scaling laws for plasma transport due toη_{i}-driven turbulence
The scale invariance technique has been employed to discuss theη_{i}-driven turbulent transport under a new fluid model developed by Kimet al [1]. Our analysis reveals that the finite Larmour radius effect plays a decisive role to determine the scaling behaviour of the energy transport under the new fluid model. However, the overall scaling of the transport coefficient remains unchanged as compared to that derived by Connor [2] under the traditional fluid model. The approximations considered by Connor [2] are qualified with additional requirements within the new fluid approach. In the dissipative case, which has not been discussed earlier, additional constraints on the power scaling laws of the transport properties are imposed due to the dissipative mechanisms in the basic governing equations.
pp 239-243 March 1996 Brief Report
Current algebra results for theB - D systems
Using the equal time commutation relations for the components of the vector and axialvector currents and keeping single particle states we obtain relations for the weak form factors for theB - D systems. In the heavy quark effective theory (HQET) limit these relations determine the Isgur-Wise function.
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