Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.

Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Hamiltonian hierarchy of pseudo-potentials

The general structure of the Hamiltonian hierarchy of the pseudo-Coulomb and pseudo-Harmonic potentials is constructed by the factorization method within the supersymmetric quantum mechanics (SQMS) formalism. The excited states and spectra of eigenfunctions of the potentials are obtained through the generation of the members of the hierarchy. It is shown that the extra centrifugal term added to the Coulomb and Harmonic potentials maintain their exact solvability.

Analytic hierarchy prioritisation of new product development activities for electronics manufacturing

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Boussinesq solitary-wave as a multiple-time solution of the Korteweg-de Vries hierarchy

We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg-de Vries hierarchy, we show that the solitary-wave of the Boussinesq equation is a solitary-wave satisfying simultaneously all equations of the Korteweg-de Vries hierarchy, each one in an appropriate slow time variable. © 1995 American Institute of Physics.

The Korteweg-de Vries hierarchy and long water-waves

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.

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.

Economic viability and selection of irrigation systems using simulation and stochastic dominance

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nutritional and social hierarchy establishment of the primitively eusocial wasp Mischocyttarus cassununga (Hymenoptera, Vespidae, Mischocyttarini) and related aspects

The results on the nutritional influence in the social hierarchy establishment among females from six colonies of Mischocyttarus cassununga show that: - there was no caste determination in the pre-imaginal period concerning ingested food quantities, however, in relation to qualification (proteins and carbohydrate) the Mann-Whitney test applied showed variation among colonies: in two colonics (colony 3, p=0.0209; colony 4, p=0.0090) the larvae which ingested a higher quantity of solid food became adults of hierarchically higher position, however in two other colonies, colony 1 (p=0.6744) and colony 2 (p=0.3367) this difference was not statistically significant; in two experimentally manipulated colonies the caste determination was observed in the imaginal phase (it was verified that the larger the food quantity consumed, the higher the assumed hierarchical position by the individuals); - adult individuals of hierarchically higher position in two colonies ingested a greater amount of solid than liquid food (Mann-Whitney; p ≤ 0.05), however in the other three colonies there was no difference. It can be seen that for all colonies (2, 3, 4, 5 and 6) the high tendency to solid food ingestion occurs. In colony 1, this data was not collected because the observation purpose was different); - inside the colony hierarchy, the older individuals were the ones that occupied higher hierarchical positions; - more than one inseminated female per colony was found in the two experimentally manipulated colonies ; - ovarian development is greater in inseminated females; - the average height of the 3rd tergite was greater for inseminated females, indicating an adaptation to accommodate larger ovary development (t-Student test; p ≤ 0.05).

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

New evidence for nucleolar dominance in hybrids of Drosophila arizonae and Drosophila mulleri

Drosophila mulleri (MU) and D. arizonae (AR) are cryptic species of the mulleri complex, mulleri subgroup, repleta group. Earlier cytogenetic studies revealed that these species have different regulatory mechanisms of nucleolar organizing activity. In these species, nucleolar organizing regions are found in both the X chromosome and the microchromosome. In the salivary glands of hybrids between MU females and AR males, there is an interspecific dominance of the regulatory system of the D. arizonae nucleolar organizer involving, in males, amplification and activation of the nucleolar organizer from the microchromosome. The authors who reported these findings obtained hybrids only in that cross-direction. More recently, hybrids in the opposite direction, i.e., between MU males and AR females, have been obtained. The purpose of the present study was to evaluate, in these hybrids, the association of the nucleoli with the chromosomes inherited from parental species in order to cytogenetically confirm the dominance patterns previously described. Our results support the proposed dominance of the AR nucleolar organizer activity over that of MU, regardless of cross-direction. ©FUNPEC-RP.