N-Soliton Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg--de Vries Equation

We concentrate on finding exact solutions for a generalized variable-coefficient Korteweg-de Vries equation of physically significance. The analytic N-soliton solution in Wronskian form for such a model is postulated and verified by direct substituting the solution into the bilinear form by virtue of the Wronskian technique. Additionally, the bilinear auto-Backlund transformation between the （ N - 1）- and N-soliton solutions is verified.     

N-Soliton-like Solution of Ito Equation

By using the extended Hirota‘s method, the N-soliton-like solution of the Ito equation is obtained. Furthermore, we also investigate the soliton-like solution interaction and find singularity.     

Variable-coefficient higher-order nonlinear Schrödinger model in optical fibers: Variable-coefficient bilinear form,Bäcklund transformation,brightons and symbolic computation

Symbolically investigated in this Letter is a variable-coefficient higher-order nonlinear Schrödinger (vcHNLS) model for ultrafast signal-routing, fiber laser systems and optical communication systems with distributed dispersion and nonlinearity management. Of physical and optical interests, with bilinear method extend, the vcHNLS model is transformed into a variable-coefficient bilinear form, and then an auto-Bäcklund transformation is constructed. Constraints on coefficient functions are analyzed. Potentially observable with future optical-fiber experiments, variable-coefficient brightons are illustrated. Relevant properties and features are discussed as well. Bäcklund transformation and other results of this Letter will be of certain value to the studies on inhomogeneous fiber media, core of dispersion-managed brightons, fiber amplifiers, laser systems and optical communication links with distributed dispersion and nonlinearity management.     

A Bilinear Backlund Transformation and Explicit Solutions for a （3＋1）-Dimensional Soliton Equation

Considering the bilinear form of a （3＋1）-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation. As an application, soliton solution and stationary rational solution for the （3＋1）- dimensional soliton equation are presented.     

Complexiton Solutions of a Special Coupled mKdV System

For a special coupled mKdV system, which can be derived from a two-layer fluid model, Hirota＇s bilinear direct method is used to construct and yield the complexiton solutions. The detailed physical properties of complexitons are filrther illustrated graphically.     

A renormalization-group study of an Ising spin-glass with annealed vacancies

Systems driven and characterized by fluctuations in density and magnetization can be realistically modeled using the Blume–Emery–Griffiths model; a spin-1 Ising model with bilinear, biquadratic, and crystal-field interactions. In this study, renormalization-group techniques are used on an exactly solvable system in which frustration is present due to competing ferromagnetic and antiferromagnetic interactions. Thus, this calculation models a spin-glass system with annealed vacancies. To determine the effects of these competing bilinear interactions, an exactly solvable frustrated hierarchical model has been constructed, similar to those introduced to study spin glasses [S.R. McKay, A.N. Berker, S. Kirkpatrick, Phys. Rev. Lett. 48 (1982) 767]. Phase diagrams have been calculated for a series of planes of constant biquadratic coupling while varying the temperature and concentration of annealed vacancies in the system. In addition, a phase diagram was produced for constant concentration of annealed vacancies as the biquadratic coupling (i.e. clustering bias) was varied. Each phase diagram reveals three qualitatively unique basins of attraction, each corresponding to a phase distinguished by a unique renormalization-group trajectory. The sink of each trajectory is interpreted to determine the nature of each phase: dense paramagnetic, dilute paramagnetic and spin-glass.     

Anisotropic magnetic exchange in orthorhombic RCu2 compounds (R = rare earth)

The magnetic excitations in the field induced ferromagnetic phase F3 of a NdCu₂ single crystal were investigated by means of inelastic neutron scattering experiments. A mean field model using the random phase approximation in connection with anisotropic magnetic bilinear R-R (R denotes a rare earth) exchange interactions is proposed to account for the observed dispersion. The relevance of this model to the analysis of the magnetic ordering process in other RCu₂ compounds is discussed. Received 21 April 1999     

Stability of SIRS system with random perturbations

Epidemiological models with bilinear incidence rate λSI usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable non-trivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is an SIRS model with or without distributed time delay influenced by random perturbations. We present the stability conditions of the disease-free equilibrium of the associated stochastic SIRS system.     

Painlevé analysis and exact solutions of the resonant Davey-Stewartson system

It is shown that the resonant Davey-Stewartson (RDS) system can pass the Painlev test. By truncating the Laurent series to a constant level term, a dependent variable transformation is naturally derived, which leads to the bilinear forms of the RDS system. From the bilinear equations, through making suitable assumptions, some new soliton solutions are obtained. Some representative profiles of the solitary waves are graphically displayed including the two-line soliton solution, “Y” soliton solution, “V” soliton solution, solitoff, etc. The solutions might be useful to describe the nonlinear phenomena in Madelung fluids, capillarity fluids, and so on.     

A generalized spin ladder in a magnetic field

We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases of spin ladder systems away from the soluble line in a magnetic field. Received 17 November 1998 and Received in final form 22 January 1999     

Mixed spin ladders with exotic ground states

We study the “mixed spin” isotropic ladder system having S=1 spins on one leg and S=1/2 spins on the other, with general-type exchange interactions between spins on neighboring rungs. A set of model Hamiltonians with exact ground states in the form of a certain matrix product wave function is obtained. We show that sufficiently strong frustration can lead to exotic singlet ground states with infinite (exponential) degeneracy. We also list a couple of rather simple models with nontrivial ground states, including a model with only bilinear exchange. Received: 2 December 1997 / Accepted: 28 January 1998     

Bäcklund transformation, nonlinear superposition formula and solutions of the Calogero equation

In this Letter, the Bäcklund transformation for the (2+1)-Calogero equation is presented in the bilinear form. Furthermore, a nonlinear superposition formula related to the transformation is proved rigorously. By the way, the Wronskian determinant solution is also derived and verified completely.     

Re-entrant phase transitions of the Blume-Emery-Griffiths model

We have investigated the spin-1 Ising model on the simple cubic lattice with bilinear, biquadratic interaction and anisotropic energy (BEG model). We have been specially interested in the case of antiferro biquadratic interaction, because the interaction will cause the competition with bilinear interaction and anisotropy. A two-sublattice ordering, so called the staggered quadrupole (SQ) phase, occurs as long as biquadratic interaction is negative large enough. We have obtained a full phase diagram in the whole interaction parameter space (for the positive bilinear interaction) by the Bethe approximation, and found several kinds of phase transitions, such as successive, re-entrant and double re-entrant transitions. These transitions are also confirmed by Monte Carlo simulations on simple cubic lattices.     

Theoretical and experimental study of Fe/Cr nanometric quasiperiodic multilayers

An experimental and theoretical study of magnetization curves of Fe/Cr nanometric magnetic films grown with the structure of the quasiperiodic Fibonacci sequence is presented. Fe ferromagnetic films with interfilm exchange coupling provided by intervening Cr non-ferromagnetic layers were grown on MgO (100) by dc magnetron sputtering at 300 ^°C. The magnetization curves were investigated using the magneto-optical Kerr effect with the external field applied along the easy axis. The theoretical approach for this system is based on a realistic phenomenological model that includes the following contributions to free magnetic energy: Zeeman, cubic magneto-crystalline anisotropy, as well as bilinear and biquadratic exchange energies. Our numerical results are in very good agreement with the experimental data.     

Phase diagrams of spin-1 Ising model with bilinear and quadrupolar interactions under magnetic field. Two-particle cluster approximation

The spin-1 Ising model with bilinear and quadrupolar short-range interactions under magnetic field is investigated within the two-particle cluster approximation. It is shown that for those values of the quadrupolar interaction when at zero magnetic field the system undergoes a temperature phase transition between quadrupolar and paramagnetic phases, a triple point may exist in the temperature vs. magnetic field phase diagrams, necessarily along with a critical point. It is also shown that the critical points in the temperature vs. magnetic field phase diagrams of the investigated model can be of three types.     

Surface-induced ordering in thin uniaxial liquid crystal films

The interface localization transition in thin uniaxial liquid crystal films with competing surface fields has been studied using Metropolis Monte Carlo simulations. The model is constructed from a lattice of continuously orientable interacting spins, and the Hamiltonian contains both bilinear and biquadratic contributions. The biquadratic contribution to the Hamiltonian is familiar from the Lebwohl-Lasher model, and accounts for the particle anisotropy in a liquid crystal. The head-tail asymmetry of the molecules in a uniaxial liquid crystal is taken into account through a bilinear contribution familiar from the classical ferromagnetic Heisenberg model with exchange anisotropy Lambda. The critical temperature T(c), characterizing the interface localization transition within the uniaxial liquid crystal film, depends strongly on the relative magnitudes of the bilinear and biquadratic interactions between the spins. For systems dominated by the biquadratic interaction, T(c) is found to be close to the bulk critical temperature of the system. But as the biquadratic interaction strength is reduced, T(c) departs markedly from the bulk critical temperature of the system.     

Rotation of magnetization in unison and langevin equations for a large spin

A single-domain ferromagnetic particle is represented as a large spin (model of rotation in unison) whose stochastic dynamics is derived from a spin-boson Hamiltonian. It is shown in the Markovian limit that thermal equilibrium exists provided that the fluctuation-dissipation theorem is supplemented by a symmetry constraint which for bilinear anisotropic and nonlinear (magnetoelastic) spin-bath coupling can only be satisfied in the underdamped limit. Only for bilinear isotropic coupling (Gilbert's theory) is it satisfied identically for arbitrary damping strength. Uniaxial and cubic symmetries are considered. For a model uniaxial crystal the thermal decay rate of M and the thermal enhancement of the macroscopic quantum tunneling rate are calculated for Gilbert and magnetoelastic dissipative couplings and compared. The effects of memory are discussed.     

Perturbed beta–gamma systems and complex geometry

We consider the equations, arising as the conformal invariance conditions of the perturbed curved beta–gamma system. These equations have the physical meaning of Einstein equations with a B-field and a dilaton on a Hermitian manifold, where the B-field 2-form is imaginary and proportional to the canonical form associated with Hermitian metric. We show that they decompose into linear and bilinear equations and lead to the vanishing of the first Chern class of the manifold where the system is defined. We discuss the relation of these equations to the generalized Maurer–Cartan structures related to BRST operator. Finally we describe the relations of the generalized Maurer–Cartan bilinear operation and the Courant/Dorfman brackets.     

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.     

Monte Carlo study of half-magnetization plateau and magnetic phase diagram in pyrochlore antiferromagnetic Heisenberg model

The antiferromagnetic Heisenberg model on a pyrochlore lattice under external magnetic field is studied by classical Monte Carlo simulation. The model includes bilinear and biquadratic interactions; the latter effectively describes the coupling to lattice distortions. The magnetization process shows a half-magnetization plateau at low temperatures, accompanied with strong suppression of the magnetic susceptibility. Temperature dependence of the plateau behavior is clarified. Finite-temperature phase diagram under the magnetic field is determined. The results are compared with recent experimental results in chromium spinel oxides.