Variational method in soliton theory

We have reported earlier the observation of a self-written waveguide inside a bulk methylene blue sensitized poly (Vinyl Alcohol) /Acrylamide photopolymer material [1]. In this work we develop a theoretical model to explain the experimental observation. We reduce the governing equations for the propagation of a low power laser beam through such a medium into the form of nonlinear Schrodinger equation with a cubic-quintic nonlinearity and solve this equation using variational method. It is found that there is agreement between experimental and theoretical results.     

The soliton mass in the sine-Gordon theory

A fully quantum mechanical variational calculation is presented for the mass of soliton and anti-soliton states in the two-dimensional sine-Gordon theory. The mass turns out to be a smooth function of the coupling parameter, and it interpolates between previously known results, which are valid at the ends of the interval of variation of this parameter.     

Quantization in presence of external soliton fields

Quantization of a Fermi field interacting with an external soliton potential is considered. Classes of interactions leading to unitarily equivalent representations of the canonical anticommutation relations are determined. Soliton-like potentials compared to trivial ones yield inequivalent representations.     

The soliton in the asymmetric scalar field theory

A new soliton solution for the asymmetric scalar field theory is obtained. The soliton is interpreted as the boson condensate drop. The phase transition is examined.     

Cancellation of the zero-mode singularities in soliton quantization theory

We give a proof of an exact cancellation of the zero-mode singularities in each order of the loop expansion determining the quantum corrections to soliton (particle-like) solutions of classical field equations. The cancellation restores an underlying symmetry broken by a specific classical solution, and is owing to the stability of the soliton with respect to small perturbation generated by the symmetry group transformations.     

KdV孤子的含时微扰理论

研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正. 关键词： KdV孤子 孤子微扰论     

Degenerate asymptotic perturbation theory

Asymptotic Rayleigh-Schrödinger perturbation theory for discrete eigenvalues is developed systematically in the general degenerate case. For this purpose we study the spectral properties ofm×m—matrix functionsA(κ) of a complex variable κ which have an asymptotic expansion εA _k κ ^k as τ→0. We show that asymptotic expansions for groups of eigenvalues and for the corresponding spectral projections ofA(κ) can be obtained from the set {A _κ} by analytic perturbation theory. Special attention is given to the case whereA(κ) is Borel-summable in some sector originating from κ=0 with opening angle >π. Here we prove that the asymptotic series describe individual eigenvalues and eigenprojections ofA(κ) which are shown to be holomorphic inS near κ=0 and Borel summable ifA _k ^* =A _k for allk. We then fit these results into the scheme of Rayleigh-Schrödinger perturbation theory and we give some examples of asymptotic estimates for Schrödinger operators.     

Phenomenological theory of soliton formation in lightly-doped polyacetylene

A phenomenological theory is introduced to investigate the influence on soliton formation of the Coulomb repulsion associated with the double occupation of the soliton's localized mid-gap state and the soliton's interaction with the iodized dopant molecule. Markedly different equilibrium parameters result for the neutral, charged-free and charged-pinned soliton forms. The frequency of the i.r. active pinning mode is predicted to be of the order of 300 cm^-1. A large zero-point motion is found for shape deformations of the soliton.     

Algebraic soliton in a ferromagnet in the presence of the magnetic field directed along the anisotropy axis

Magnetic solitons in a one-dimensional ferromagnet with easy-plane anisotropy are considered. Algebraic solitons are discussed and the conditions of existence of such solitons are investigated.     

Random evolution and coherence degradation of a high-order optical soliton train in the presence of noise

The intrinsic evolution of a high-order soliton described by the nonlinear Schr?dinger equation is initiated by a self-four-wave mixing effect (or modulational instability) and recurs neatly every soliton period. We show that when there is noise such as amplified spontaneous emission, however, a high-order soliton evolves randomly and independently and is distorted because the evolution is initiated by noise. Thus the time and the frequency coherence of a soliton pulse train are both greatly degraded.     

Scattering theory of defects in crystals

The theory of scattering is applied here to the problem of the electronic states of impurities. The S, T and K matrices, the Lippman-Schwinger and Dyson equations are used to formulate the problem. The standard concepts, methods and results of scattering theory applied to impurities discussed include the scattering amplitude, the Fredholm determinant, dispersion relations, Regge poles, Levinson's theorem and Fadeev's equations. Physical consequences considered are the change in density of states, eigenstates and transport theory. The necessity of extending the scattering formalism to many-body theory is discussed. The relation between scattering theory and other methods of impurity theory is also mentioned.     

Scattering theory in quantum field theory in configuration space

The recent analysis of the propagation of relativistic particles inspacetime and their localization problem is used to develop scattering theory in quantum field theory inconfiguration space. An explicit functional expression is derived for the underlying transition amplitudes having a consistent probabilistic interpretation. Some of the basic ingredients in the analysis are the functional approach developed earlier for transition amplitudes and the amplitudes for stimulated emission of particles by external sources in spacetime.     

Hydrodynamic theory of the sine-Gordon soliton lattice and soliton propagation in 3HeA

A theory is developed which describes the slow time and space evolution of a sine-Gordon soliton lattice, taking dissipation into account. The theory is applied to the experiment on soliton propagation in ³HeA. The role of the spin superflow transverse to the soliton propagation direction is discussed.     

Dark soliton switching in an NLDC in the presence of higher-order perturbative effects

Dark soliton switching in a nonlinear directional coupler in the presence of intermodal dispersion, cross-phase modulation (CPM), third-order dispersion, Raman effect, and self-steepening effect is reported for the first time. It is shown that, with the exception of CPM, all of the other perturbative effects have almost no effect on the switching characteristics of the dark soliton switch, which is an improvement over the corresponding bright soliton switch. Although the CPM increases the critical power of dark soliton switching, the soliton pulse remains stable inside the coupler during its propagation.     

Microscopic theory of soliton propagation in4He films

A microscopic theory has been provided for propagation of solitons in superfluid⁴He films at temperatureT=0°K.