BRS cohomology of the supertranslations inD=4

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator . We find that the cohomology of this operator depends on a spin-orbit coupling in anSU(2) group and has a quite complicated structure. This spin-orbit type coupling will turn out to be basic in the cohomology of supersymmetric field theories in general.     

Self-Induced Transparency Solitons and Dissipative Solitons in Microwave Electronic Systems

Radiophysics and Quantum Electronics - Solitons are a well-studied subject in many domains of nonlinear physics, including hydrodynamics, plasma physics, optics, etc. However, it has been...     

Cusp and Regular Ion-Acoustic Solitons

Cups and regular smooth solitons are studied using the fluid model in cylindrical geometry for parallel propagating ion-acoustic waves in a low β plasma. It is found that smooth solitons only occur in the supersonic regime, whereas cusp solitons occur both in supersonic and subsonic regimes. In the supersonic regime, the amplitude and the width of cusp solitons increase when the Mach number M increases and initial electric field E ₀ decreases. However, the amplitude of smooth regular solitons increases and their width decreases when E ₀ increases and M decreases. For the subsonic case, both the amplitude as well as the width of a cusp solitons increase when M increases and E ₀ decreases. Corresponding to these cusp and regular solitons, bipolar electric field structures are also studied. These results may be helpful in understanding the properties of ion-acoustic regular and cusp solitons in space plasmas.     

Solitons and polarization mode dispersion

Analytical expressions are presented for Manakov solitons perturbed by polarization mode dispersion (PMD). Comparison is made with computer simulations. Dispersion-managed solitons are also studied. It is concluded that at high bit rates solitons are superior to linear return-to-zero propagation with regard to PMD.     

Solitons and vortices in lasers

We give in this article the mathematical background for pattern formation in nonlinear active resonators, elucidating the relation of optics with other fields of physics, and demonstrate experimentally the existence, properties, and dynamics of: (i) vortices in lasers, (ii) bright spatial solitons in lasers with saturable absorber, and (iii) spatial solitons in degenerate parametric mixing. All these structures are by definition bistable so that they are potentially useful for parallel optical information processing. Received: 8 June 1998     

Solitons and Deformed Lattices I

Abstract

We study a model describing some aspects of the dynamics of biopolymers. The models involve either one or two finite chains with a number N of sites that represent the “units” of a biophysical system. The mechanical degrees of freedom of these chains are coupled to the internal degrees of freedom through position dependent excitation transfer functions. We reconsider the case of the one chain model discussed by Mingaleev et al. and present new results concerning the soliton sector of this model. We also give new (preliminary) results in the two chain model in which case we have introduced an interaction potential inspired by the Morse potential.     

Solitons and Vortices in Plasmas

The various types of nonlinear wave solutions in plasmas are reviewed. First, the generation, pro- pagation, and stability of solitary waves are demonstrated for some simple examples. Then, relevant two-and three-dimensional models for Langniuir solitons are proposed and investigated. The collapse as an effective dissipation mechanism in plasmas is discussed in detail. Finally, simple models of two-dimensional vortex motion and their consequences are considered.     

Solitons and Fractal Kerr Response

Optical solitary waves that propagate in a Kerr medium exhibiting a power-law nonlocal response are studied analytically. The first-principles stability analysis based on quantum field theory shows that within the whole range of the exponent (the fractal dimension) the solitary wave can be stabilized.     

Spin Statistics and CPT for Solitons

Conditions are analysed under which the statistics of soliton sectors of massive two-dimensional field theories can be properly defined. A soliton field algebra is defined as a crossed product with the group of soliton sectors. In this algebra, the nonlocal commutation relations are determined and weak locality, spin statistics and CPT theorems are proven. These theorems depart from their usual appearance due to the broken symmetry connecting the inequivalent vacua. An interpretation of these results in terms of modular theory is given. For the neutral subalgebra of the soliton algebra, the theorems hold in a familiar form, and twisted duality is derived.     

Acousto-Optic Solitons in Fibers

It is shown that the deceleration of light pulses down to the velocity of a sound value can be realized in a case of unidirectional parametric interaction of two electromagnetic waves with an acoustic one in the regime of forming three wave acousto-optic solitons. This nonlinear acousto-optic interaction can be realized in long distance systems like fibers. As the result of such an interaction, two types of acousto-optic envelope solitons can propagate in fibers. Modulation of the amplitude of the electromagnetic pump wave can control the soliton velocity.     

Dynamics of Sine-Gordon Solitons

After reviewing a few physical examples in whichthe sine-Gordon equation arises as the governingdynamical equation, we discuss various solutionsexhibiting multisoliton dynamics. Interaction ofsolitons and the corresponding velocity-dependentinteraction potentials are derived and discussed.Numerical experiments are carried out in order to studykink dynamics in an inhomogeneous medium. Finally, weintroduce two kinds of generalized sine-Gordon equationsand discuss their properties.