Nonlinear dynamics of a quasi-one-dimensional spiral structure

The nonlinear dynamics of solitons and spin waves in spiral magnets without inversion centers is investigated using the sine-Gordon model. The possibility of finding solitons in spiral structures is discussed.     

Envelope solitons of electromagnetic spin waves in an artificial layered multiferroic

The nonlinear wave properties of an artificial multiferroic medium consisting of a ferroelectric layer and a ferromagnetic layer have been studied. The simultaneous effect of wave nonlinearities of both layers on the formation and propagation of envelope solitons has been analyzed. It has been shown that bright envelope solitons of electromagnetic spin waves can appear in such a medium owing to the wave nonlinearity of ferroelectric layer. In order to confirm the theoretical results, the coefficients of the nonlinear Schrödinger equation have been calculated and this equation has been solved numerically.     

Observation of self-generation of dark envelope solitons for spin waves in ferromagnetic films

We have performed experiments in which self-generation of dark envelope solitons for spin waves at microwave frequencies were obtained. Stable self-generation of dark solitons was observed in a ring consisting of tangentially magnetized yttrium iron garnet film and a microwave signal amplifier. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 229–233 (10 August 1998)     

Coupled spin, elastic, and electromagnetic waves in the magnetic of a ferromagnetic spiral phase

The spectrum of coupled spin, elastic, and electromagnetic waves in the magnetic of a ferromagnetic spiral phase is investigated. The frequency dependences of the reflection coefficient of electromagnetic waves from the surface of a semi-infinite magnet for different angles of the spiral are obtained. An acoustic analog of the Faraday effect in the magnetics of a ferromagnetic spiral phase is considered.     

Thermodynamics of a quasi-one-dimensional spin system for molecule-based ferrimagnets

A physical picture of electron spin alignments in organic molecule-based ferrimagnets is given from numerical calculations of magnetic specific heat (C) and magnetic susceptibility (χ) as functions of temperature and static magnetic field (B) in terms of an Ising Hamiltonian for an alternating spin chain. The double-peak structure of specific heat appears for different parameter ratios and different magnetic field B, indicating that one peak originates from the ferromagnetic nature and the other from the antiferromagnetic nature. Meanwhile, we study successively the influence of intermolecular and intramolecular interaction on the magnetic susceptibility, showing that the ferromagnetic spin alignment in the alternating molecular chains of biradicals and monoradicals is equivalent to the ferromagnetic alignment of the effective S=1/2 spins. Our results are consistent with those of the Quantum Monte Carlo simulations and the exact diagonalization method and in qualitative agreement with the experimental ones.     

Scattering of quasi-one-dimensional solitons on impurities in large Josephson junctions

Fluxon transmission through impurities of different shape in a quasi-one-dimensional long Josephson junction is investigated. The junction width is significantly less than its length but, at the same time, is of the order of the Josephson penetration length _λJ${\lambda }_J$ or exceeds it. The retrapping current on the impurities of the point, line and rectangular shape is computed as a function of the junction width both numerically and analytically. Good agreement between the analytic formulae and the numerical simulation results for the intermediate (several _λJ${\lambda }_J$) junction width is observed.     

Rogue waves and solitons on a cnoidal background

Solutions of the nonlinear Schrödinger equation, appearing as rogue waves on a spatially-periodic background envelope, are obtained using the Darboux transformation scheme. Several particular examples are illustrated numerically. These include soliton and breather solutions on a periodic background as well as higher-order structures. The results enrich our knowledge of possible analytic solutions that describe the appearance of rogue waves in a variety of situations. This work is prepared on the occasion of Prof. Helmut Brand's 60th birthday. He has made significant contributions to the science of solitons and his ideas have inspired our research into localised formations in various physical contexts.     

Nonlinear surface waves and solitons

First a general introduction on the notion of surface waves on solids (types of different waves), a reminder on the simplest familiar nonlinear dispersive model equations, and another on the basic equations of nonlinear elasticity are given. Then attention is focused on the linear surface wave problem. The main properties of nonlinear surface waves in the absence of dispersion are studied next by use of several asymptotic techniques. The additional effects of dispersion are then considered and combined with those of nonlinearity with an emphasis on the case of so-called shear-horizontal surface waves and solitary-wave solutions for envelope signals. Finally, typical nonlocality is introduced for nonlinear Rayleigh surface waves, and general comments on more general two-dimensional (in propagation space) nonlinear strain waves on structures are evoked by way of conclusion.     

Bloch-Ising phase transition in spin solitons

Heisenberg spin chains with ferromagnetic nearest-neighbor coupling and an easy axis of magnetisation are considered in the classical limit. The critical ratioa _c between the anisotropy coefficient and the exchange integral for which the 180°-Blochtype soliton undergoes a phase transition to an Ising-type soliton is calculated by an exact analytical algorithm. For chains including 2N=4,6,8,... spins, one finds a sequencea _c (2N) which converges rapidly to the valuea _c()=2/3 (e.g.a _c (12)=0.66664) marking the phase transition from a Bloch- to an Ising-structure of the soliton in an infinite chain.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Nonlinear spiral waves in a galactic disk

An analytical solution of the nonlinear dynamic equations for a galactic disk is found. This solution describes the spiral design of spiral galaxies. The logarithmic profile of the spiral design and relatively larger density fluctuations as compared to velocity-field fluctuations are explained. Breaking of the obtained solution takes place for a certain critical amplitude. This can be a mechanism for the formation of galactic shocks and narrow star formation regions.     

Surface spiral waves in a filamentary vortex

Second-order [ O(k(2)), k = omega/c] nondipole effects in soft-x-ray photoemission are demonstrated via an experimental and a theoretical study of angular distributions of neon valence photoelectrons in the 100-1200 eV photon-energy range. A newly derived theoretical expression for nondipolar angular distributions characterizes the second-order effects using four new parameters with primary contributions from pure-quadrupole and octupole-dipole interference terms. Independent-particle calculations of these parameters account for a significant portion of the existing discrepancy between experiment and theory for Ne 2p first-order nondipole parameters.     

Phonon scattering in quasi-one-dimensional structure

We introduce a model to study a symmetric nanocontact, whereby its mechanical properties can be analyzed via the vibration spectra. The model system consists of two groups of triple semi-infinite atomic chains joined by atoms in between. The matching method theoretical approach is used to calculate the coherent reflection and transmission scattering probabilities, the characteristic vibration Green functions and densities of states (DOS), for the vibration components of the individual atomic sites that constitute a complete representation of the nanocontact domain boundaries. The nanocontact observables are numerically calculated for different cases of elastic hardening and softening, to investigate how the local dynamics can respond to changes in the microscopic environment on the nanocontact domain. The analysis of the vibration spectra and the DOS demonstrate the fluctuations, related to Fano resonances, due to the coherent coupling between traveling phonons and the localized vibration modes in the nanocontact domain.     

The influence of continuous-wave pumping on the propagation of envelope solitons of magnetostatic spin waves

The influence of continuous-wave pumping on the propagation of solitons of magnetostatic spin waves is studied. It is shown that, at certain conditions when the frequency of the continuously excited wave falls into the spectrum of a soliton-like pulse, the nonlinear interaction results in soliton decay. Numerical calculations of this effect are presented.     

Varieties of solitons and solitary waves

A summary is presented of the principal types of completely integrable partial differential equations having soliton solutions. Each type is derived from an appropriate physical model of an electromagnetic wave problem, with the intention to show how known mathematical results apply to a coherent class of physical problems in electromagnetic waves. The non-linear Schrödinger (NS) equation appears when the induced non-linear dielectric polarization is expanded in a series of powers of the electric field, only the linear and third-order polarizations are retained, and the temporal spectrum of the wave is a narrow band far removed from any resonance of the medium. The sine-Gordon equation appears from a similar optical model of propagation in a dielectric consisting of identical 2-level atomic systems, but resonance occurs between the carrier frequency of the wave and the transition frequency of the atoms. The Boussinesq and Korteweg– de Vries equations appear at different levels of approximation to a potential wave on a transmission line having a non-linear capacitance such that the charge stored is a non-linear function of the line potential. In all cases the evolution variable is the propagation distance; the transverse variable is time, but in the case of the NS equation it may alternatively be a spatial coordinate, giving rise to the possibility of spatial solitons as well as temporal solitons for NS-type problems. Two examples are derived of non-integrable Hamiltonian systems having spatial solitary waves, namely the second-order cascade interaction and vector spatial solitary waves of the third-order interaction, and a brief survey of the analytical solutions for the plane waves and solitary waves of these two types is presented. Finally, the addition of a second spatial dimension to the non-linear transmission line problem leads to the Kadomtsev–Petviashvili equations, and a further approximation for weakly modulated travelling waves leads to the Davey–Stewartson equations. Both of these completely integrable systems support combined spatial–temporal solitons.