In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed $(3+1)$-dimensional, integrable, and relativistically invariant field theory. Two integers label family have found. Their product is equal to charge which provides a lower bound soliton's finite energy. The are constructed in terms toroidal coordinates shown form linked closed vortices.

A deformation parameter of a bihamiltonian structure hydrodynamic type is shown to parameterize different extensions the AKNS hierarchy include negative flows. This construction establishes purely algebraic link between, on one hand, two realizations first flow model and, other, two-component generalizations Camassa-Holm and Dym equations. The equations can be obtained from order Hamiltonians constructed Lenard relations recursively applied Casimir Poisson bracket type. positive...

The energy levels of boxed-in harmonic and inverted oscillators are constructed from the perturbative asymptotic solutions that valid in limits small large sizes, respectively. In order to obtain expressions for which boxes any size, authors use Pade approximants as interpolations between solutions. Special attention is paid lowest levels. accuracy range validity each type solution illustrated by comparing them with exact obtained constructing diagonalising matrix Hamiltonian system basis...

Logarithmic singular potentials are considered to test the applicability of peratization technique. It is shown that if one sums up leading terms in each order perturbation series no finite results can be obtained.

Expressing the generalised zeta function Sigma n omega n-s in terms of 'partition function' ne- alpha (n), authors show this paper why they obtain same answer for Casimir effect (in many physical situations) if use, alternatively, analytic continuation procedure or take first derivative above partition and make to 0+ with neglect all pole =O.

Superconvergent sum rules are written for the optical constants of nonmagnetic materials. First a generalization some results Altarelli et al. is attained by means Liu and Okubo technique. In particular, we have set inequalities. Second, new superconvergent obtained considering suitable powers constants. They characterized strong damping high frequencies rules. Sum involving higher electric conductivity also indicated.

In this paper we provide an algebraic construction for the negative even mKdV hierarchy which gives rise to time evolutions associated graded Lie structure.We propose a modification of dressing method, in order incorporate non-trivial vacuum configuration and construct deformed vertex operator ŝl(2), that enable us obtain explicit systematic solutions whole grade equations.

The introduction of defects is discussed under the Lagrangian formalism and Backlund transformations for N=1 super sinh-Gordon model. Modified conserved momentum energy are constructed this case. Some explicit examples different solitons solutions discussed. Lax formulation within space split by defect leads to integrability model henceforth existence an infinite number constants motion

First Page

Using the fact that Miura transformation can be expressed in form of gauge connecting KdV and mKdV equations, we discuss derivation B\"acklund its Miura-gauge both hierarchies.

A bstract The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas theoretical physics. While positive part well known, this paper we consider an affine Lie algebraic construction for its negative part. We show that original Miura transformation can be extended to gauge implies new types relations among flows mKdV hierarchies. Contrary flows, such “gauge-Miura” correspondence becomes...

We present a construction of class rational solutions the Painlev\'e V equation that exhibit two-fold degeneracy, meaning there exist two distinct share identical parameters. The fundamental object our study is orbit translation operators $A^{(1)}_{3}$ affine Weyl group acting on underlying seed solution only allows action some symmetry operations. By linking points this to solutions, we establish conditions for such degeneracy occur after involving in additional B\"acklund transformations...

An affine sl(n+1) algebraic construction of the basic constrained KP hierarchy is presented. This analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and Lax formulation it shown that these approaches are equivalent. The model recognized to be generalized non-linear Schrödinger (GNLS) used as a building block for new class hierarchies. These hierarchies connected via similarity-Bäcklund transformations interpolate between GNLS multi-boson...

We formulate the constrained KP hierarchy (denoted by \cKP$_{K+1,M}$) as an affine ${\widehat {sl}} (M+K+1)$ matrix integrable generalizing Drinfeld-Sokolov hierarchy. Using algebraic approach, including graded structure of generalized hierarchy, we are able to find several new universal results valid for \cKP In particular, our method yields a closed expression second bracket obtained through Dirac reduction any untwisted Kac-Moody current algebra. An explicit example is given case...