The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation

We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.

Non-anomalous generalized chiral Schwinger model

Recently, Basseto and Griguolo1 did a perturbative quantization of what they called a generalized chiral Schwinger model. As a consequence of the kind of quantization adopted, some gauge-dependent masses raised in the model. On the other hand, we discussed the possibility of introducing a generalized Wess-Zumino term,2 where such gauge-dependent masses did appear. Here we intend to show that one can construct a non-anomalous version of a model which include that, presented by Basseto and Griguolo as a particular case, by adding to it a generalized Wess-Zumino term, as proposed in Ref. 2. So we conclude that it is possible to construct a gauge-invariant extension of the model quoted in Ref. 1, and this can be done through a Wess-Zumino term of the type proposed in Ref. 2.

Generalized simulated annealing: Application to silicon clusters

We have compared the recently introduced generalized simulated annealing (GSA) with conventional simulated annealing (CSA). GSA was tested as a tool to obtain the ground-state geometry of molecules. We have used selected silicon clusters (Sin, n=4-7,10) as test cases. Total energies were calculated through tight-binding molecular dynamics. We have found that the replacement of Boltzmann statistics (CSA) by Tsallis's statistics (GSA) has the potential to speed up optimizations with no loss of accuracy. Next, we applied the GSA method to study the ground-state geometry of a 20-atom silicon cluster. We found an original geometry, apparently lower in energy than those previously described in the literature.

A generalized theory of electrical characteristics of schottky barriers for amorphous materials

In the present paper, we discuss a generalized theory of electrical characteristics for amorphous semiconductor (or insulator) Schottky barriers, considering: (i) surface states, (ii) doping impurity states at a single energy level and (iii) energetically distributed bulk impurity states. We also consider a thin oxide layer (≈10 Å) between metal and semiconductor. We develop current versus applied potential characteristics considering the variation of the Fermi level very close to contact inside the semiconductor and decrease in barrier height due to the image force effect as well as potential fall on the oxide layer. Finally, we discuss the importance of each parameter, i.e. surface states, distributed impurity states, doping impurity states, thickness of oxide layer etc. on the log I versus applied potential characteristics. The present theory is also applicable for intimate contact, i.e. metal-semiconductor contact, crystalline material structures or for Schottky barriers in insulators or polymers.

Some comments on the bi(tri)-Hamiltonian structure of generalized AKNS and DNLS hierarchies

We give the correct prescriptions for the terms involving ∂ -1 xδ(x - y), in the Hamiltonian structures of the AKNS and DNLS systems, necessary for the Jacobi identities to hold. We establish that the sl(2) and sl(3) AKNS systems are tri-Hamiltonians and construct two compatible Hamiltonian structures for the sl(n) AKNS system. We give a method for the derivation of the recursion operator for the sl(n + 1) DNLS system, and apply it explicitly to the sl(2) case, showing that such a system is tri-Hamiltonian. © 1998 Elsevier Science B.V.

Linearizability of the perturbed Burgers equation

We show in this report that the perturbed Burgers equation ut = 2uux + uxx + ε(3 α1u2ux + 3 α2uuxx + 3 α3u2 x + α4uxxx) is equivalent, through a near-identity transformation and up to O(ε), to a linearizable equation if the condition 3 α1 - 3 α3 - 3/2α2 + 3/2α4 = 0 is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. We show, furthermore, that nonlinearizable cases lead to perturbative expansions with secular-type behavior. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.

Gel'fand-Levitan equation for deletion of states from Coulomb spectra

The Gel'fand-Levitan formalism is used to study how a selected set of bound states can be eliminated from the spectrum of the Coulomb potential and also how to construct a bound state in the Coulomb continuum. It is demonstrated that a sizeable quantum well can be produced by deleting a large number of levels from the s spectral series and the edge of the Coulomb potential alone can support the von Neumann-Wigner states in the continuum. © 1998 Elsevier Science B.V.

Two-body Dirac equation approach to the deuteron

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ = 1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

Generalized polarizabilities and electroexcitation of the nucleon

Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer Q2. In particular, the sum of the generalized electric and magnetic polarizabilities ∑ = α + β and the spin polarizability γ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predictions of chiral perturbation theory. © 1999 Elsevier Science B.V. All rights reserved.

Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved.

Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrödinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schrödinger equation. A particular scaling is used in the equation, which permits us to evaluate the wave-function normalization after the numerical solution. We have a two-point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, be equal for large distances. In order to obtain fast convergence, the secant method is used. © 1999 The American Physical Society.

Extended Hierarchical Censored Production Rules (EHCPRs) system: An approach toward generalized knowledge representation

One common problem in all basic techniques of knowledge representation is the handling of the trade-off between precision of inferences and resource constraints, such as time and memory. Michalski and Winston (1986) suggested the Censored Production Rule (CPR) as an underlying representation and computational mechanism to enable logic based systems to exhibit variable precision in which certainty varies while specificity stays constant. As an extension of CPR, the Hierarchical Censored Production Rules (HCPRs) system of knowledge representation, proposed by Bharadwaj & Jain (1992), exhibits both variable certainty as well as variable specificity and offers mechanisms for handling the trade-off between the two. An HCPR has the form: Decision If(preconditions) Unless(censor) Generality(general_information) Specificity(specific_information). As an attempt towards evolving a generalized knowledge representation, an Extended Hierarchical Censored Production Rules (EHCPRs) system is suggested in this paper. With the inclusion of new operators, an Extended Hierarchical Censored Production Rule (EHCPR) takes the general form: Concept If (Preconditions) Unless (Exceptions) Generality (General-Concept) Specificity (Specific Concepts) Has_part (default: structural-parts) Has_property (default:characteristic-properties) Has_instance (instances). How semantic networks and frames are represented in terms of an EHCPRs is shown. Multiple inheritance, inheritance with and without cancellation, recognition with partial match, and a few default logic problems are shown to be tackled efficiently in the proposed system.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

Galilean covariance and the Duffin-Kemmer-Petiau equation

We use a five-dimensional approach to Galilean covariance to investigate the non-relativistic Duffin-Kemmer-Petiau first-order wave equations for spinless particles. The corresponding representation is generated by five 6 × 6 matrices. We consider the harmonic oscillator as an example.