Solitary waves on vortex lines in Ginzburg-Landau models for the example of Bose-Einstein condensates

Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary waves is shown in the momentum (p)-substitution energy (Epsilon) plane with p-->0.09 rho kappa(3)/c(2), Epsilon-->0.091 rho kappa(3)/c as U-->c, where rho is the density, c is the speed of sound, kappa is the quantum of circulation, and U is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particular, it is shown that during collapse the vortex core becomes significantly compressed, and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line.     

Solitary wave interactions in lattice systems with pure higher-order nonlinearity

In this paper, we investigate in detail the interactions of solitary waves in lattice systems with interaction potential V(q)=qⁿ/n, where n is 4,6,8…, through their all possible collision types, and establish a quantitative connection between the scattering property of solitary waves and the chaotic dynamics of the systems. Kink and antikink are excited in such lattice systems and the variation of their scattering effect with n is concerned. After a kink-antikink collision, the dominant interaction in the systems, if n is small, is that solitary waves pass through each other and the scattering effect increases with n; if n is large, solitary waves reflect back sometimes due to the influence of phase and this leads to a decrease of the scattering effect with n. The largest Lyapunov exponents of systems at fixed energy density first increase and then decrease with n, which is consistent with a variation of the scattering effect. The application of the special scattering behaviors between kink and antikink in information propagation is also discussed.     

A(2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution

In this paper,we investigate a(2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids.We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasigeostrophic potential vorticity equation with dissipation and topography under the generalized beta effect,and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method.Through the analysis of this model,it is found that the generalized beta effect and basic topography can induce nonlinear waves,and slowly varying topography is an external impact factor for Rossby waves.Additionally,the conservation laws for the mass and energy of solitary waves are analyzed.Eventually,the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method.Based on the solitary wave solutions obtained,we discuss the effects of dissipation and slowly varying topography on Rossby solitary waves.     

Production of Alfvén waves by a rapidly expanding dense plasma

The expansion of a dense (initially, n(lpp)/n(0)>1) laser-produced plasma into an ambient magnetized plasma ( n(0) = 2 x 10(12) cm(-3)) capable of supporting Alfvén waves has been studied. The interaction results in the production of shear Alfvén waves as well as large density perturbations (Delta n/n(0) approximately 0.3) associated with the moving dense plasma. The waves propagate away from the target and are observed to become plasma-column resonances. Spatial patterns of the wave magnetic fields are measured and are used to estimate the coupling efficiency of the laser energy and the kinetic energy of the dense plasma into wave energy.     

Coupled Korteweg de Vries solitary wave of superfluid Bose-Fermi mixture

In this paper, the solitary waves in superfluid Bose-Fermi mixture are investigated under the limited case of a BEC regime, a BCS regime and unitarity. By using the transverse perturbation method, a coupled Korteweg de Vries (KdV) equation for the nonlinear solitary waves is derived. It is found that the scattering length between bosons and fermions has strong effect on the characters of the coupled solitary wave.     

孤子内波导致海洋环境噪声垂直指向性异常分析

依据近场波数积分、远场耦合简正波相结合的二维噪声场模型,侧重理论研究孤子内波所在扇区,环境噪声垂直阵响应的变化,分析了某些孤子内波情形下垂直阵环境噪声水平凹槽变深这一异常现象的原因:孤子内波离垂直阵较近时,远离内波的海面噪声源多,其激发的简正波能量由低号耦合到高号,在垂直阵处高号简正波能量对环境噪声场贡献增大,导致环境噪声水平凹槽加深;对于大尺度、多波包孤子内波,其范围相对较大,内波所在区的局部简正波本征值和本征函数产生的变化影响显著,使低号简正波衰减变快,而高号衰减慢,导致接收阵处高号简正波能量增加,低号简正波变弱,这样,无论孤子内波群靠近或离接收阵远,都将使垂直阵环境噪声水平凹槽加深。      

Bifurcation and stability of dynamical structures at a current instability

We investigate bifurcation and stability of nonuniform current states at a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The system is described by balance equations for momentum and energy densities of the carriers. These transport fields are coupled to Maxwell's equations. The uniform stationary current state is unstable against long-wavelength dielectric relaxation modes at a critical field. We find that the softening of these modes gives rise to a family of periodic travelling waves and to a solitary solution (dipole domain). We show that the periodic travelling waves are unstable, wheras the dipole domain can be stabilized by coupling the sample to a suitable external circuit, if the static impedance of the sample in the domain state is negative. The model describes therefore a discontinuous nonequilibrium transition to a large amplitude domain state.Work Supported by the Swiss National Science Foundation     

手征SU(3)夸克模型研究低能Nπ散射相移

在手征,SU(3),夸克模型中,通过求解共振群方程动力学地研究了同位旋,I=1/2,和,I=3/2,道,Nπ,的,S,波和,P,波低能弹性散射相移.所用的模型参数由基态八重态和十重态重子的能量定出, 并能给出不同分波的,KN,散射相移.除了有明显共振态的道以外, 计算得到的各个分波的,Nπ,散射相移和实验值定性一致.     

Vortex rings and solitary waves in trapped Bose–Einstein condensates

We discuss nonlinear excitations in an atomic Bose–Einstein condensate which is trapped in a harmonic potential. We focus on axially symmetric solitary waves propagating along a cylindrical condensate. A quasi one-dimensional dark soliton is the only nonlinear mode for a condensate with weak interactions. For sufficiently strong interactions of experimental interest solitary waves are hybrids of one-dimensional dark solitons and three-dimensional vortex rings. The energy-momentum dispersion of these solitary waves exhibits characteristics similar to a mode proposed sometime ago by Lieb in a strictly 1D model, as well as some rotonlike features. We subsequently discuss interactions between solitary waves. Head-on collisions between dark solitons are elastic. Slow vortex rings collide elastically but faster ones form intermediate structures during collisions before they lose energy to the background fluid. Solitary waves and their interactions have been observed in experiments. However, some of their intriguing features still remain to be experimentally identified.     

Two-dimensional bright solitons in dipolar Bose-Einstein condensates

We analyze the physics of bright solitons in 2D dipolar Bose-Einstein condensates. These solitons, which are not possible in short-range interacting gases, constitute the first realistic proposal of fully mobile stable 2D solitons in ultracold gases. In particular, we discuss the necessary conditions for the existence of stable 2D bright solitary waves by means of a 3D analysis of the lowest-lying excitations. We show that the anisotropy of the dipolar potential is crucial, since sufficiently large dipolar interactions can destabilize the 2D soliton. Additionally, we study the scattering of solitary waves, which, contrary to the contact-interacting case, is inelastic and could lead to fusion of the waves. Finally, the experimental possibilities for observability are discussed.     

Changing shapes: adiabatic dynamics of composite solitary waves

We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite nonlinear non-dispersive waves points to variations in shape.     

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.     

Anomalous high-energy spin excitations in the high-Tc superconductor-parent antiferromagnet La₂CuO₄

Inelastic neutron scattering is used to investigate the collective magnetic excitations of the high-temperature superconductor-parent antiferromagnet La2CuO4. We find that while the lower energy excitations are well described by spin-wave theory, including one- and two-magnon scattering processes, the high-energy spin waves are strongly damped near the (1/2, 0) position in reciprocal space and merge into a momentum dependent continuum. This anomalous damping indicates the decay of spin waves into other excitations, possibly unbound spinon pairs.     

The bifurcation and peakons for the special C (3, 2, 2) equation

In this paper, we investigate a special C(3, 2, 2) equation $$\begin{array}{@{}rcl@{}} u_{t}+ku_{x}-u_{xxt}+3(u^{3})_{x}=u_{x}(u^{2})_{xx}+u(u^{2})_{xxx}. \end{array} $$ The bifurcation and some new exact representations of peakons, bell-shaped solitary wave solutions and periodic cusp wave solutions for the equation are obtained using the qualitative theory of dynamical systems. It is shown that the peakons are actually the limit of bell-shaped solitary waves and periodic cusp waves. Moreover, a new characteristic of non-smooth solutions, two peakons coexisting for the same wave speed, is found. Some previous results are extended.     

A new model for algebraic Rossby solitary waves in rotation fluid and its solution

A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space.Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves,the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves,the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.     

Generation of Solitary Rossby Waves by Unstable Topography

The effect of topography on generation of the solitary Rossby waves is researched.Here,the topography,as a forcing for waves generation,is taken as a function of longitude variable x and time variable t,which is called unstable topography.With the help of a perturbation expansion method,a forced mKdv equation governing the evolution of amplitude of the solitary Rossby waves is derived from quasi-geostrophic vorticity equation and is solved by the pseudospectral method.Basing on the waterfall plots,the generational features of the solitary Rossby waves under the influence of unstable topography and stable topography are compared and some conclusions are obtained.     

Decay of solitons in an isotropic collisionless quasineutral plasma with isothermal pressure

Soliton-type solutions of the complete unreduced system of transport equations describing the plane-parallel motions of an isotropic collisionless quasineutral plasma in a magnetic field with constant ion and electron temperatures are studied. The regions of the physical parameters for fast and slow magnetosonic branches, where solitons and generalized solitary waves—nonlocal soliton structures in the form of a soliton “core” with asymptotic behavior at infinity in the form of a periodic low-amplitude wave—exist, are determined. In the range of parameters where solitons are replaced by generalized solitary waves, soliton-like disturbances are subjected to decay whose mechanisms are qualitatively different for slow and fast magnetosonic waves. A specific feature of the decay of such disturbances for fast magnetosonic waves is that the energy of the disturbance decreases primarily as a result of the quasistationary emission of a resonant periodic wave of the same nature. Similar disturbances in the form of a soliton core of a slow magnetosonic generalized solitary wave essentially do not emit resonant modes on the Alfvén branch but they lose energy quite rapidly because of continuous emission of a slow magnetosonic wave. Possible types of shocks which are formed by two types of existing soliton solutions (solitons and generalized solitary waves) are examined in the context of such solutions.     

Solitary wave complexes in two-component condensates

Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction strengths. Several families of solitary wave complexes are found: (1) vortex rings of various radii in each of the components; (2) a vortex ring in one component coupled to a rarefaction solitary wave of the other component; (3) two coupled rarefaction waves; (4) either a vortex ring or a rarefaction pulse coupled to a localized disturbance of a very low momentum. The continuous families of such waves are shown in the momentum-energy plane for various values of the interaction strengths and the relative differences between the chemical potentials of two components. Solitary wave formation, their stability, and solitary wave complexes in two dimensions are discussed.     

Solitary waves in the granular chain

Solitary waves are lumps of energy. We consider the study of dynamical solitary waves, meaning cases where the energy lumps are moving, as opposed to topological solitary waves where the lumps may be static. Solitary waves have been studied in some form or the other for nearly 450 years. Subsequently, there have been many authoritative works on solitary waves. Nevertheless, some of the most recent studies reveal that these peculiar objects are far more complex than what we might have given them credit for. In this review, we introduce the physics of solitary waves in alignments of elastic beads, such as glass beads or stainless steel beads. We show that any impulse propagates as a new kind of highly interactive solitary wave through such an alignment and that the existence of these waves seems to present a need to re-examine the very definition of the concept of equilibrium. We further discuss the possibility of exploiting nonlinear properties of granular alignments to develop exciting technological applications.     

Rarefactive ion-acoustic electrostatic solitary structures in nonthermal plasmas

An investigation has been made of ion-acoustic solitary waves in an unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. The properties of stationary solitary structures are briefly studied by the pseudo-potential approach, which is valid for arbitrary amplitude waves, and by the reductive perturbation method which is valid for small but finite amplitude limit. The time evolution of both compressive and rarefactive solitary waves, which are found to coexist in this nonthermal plasma model, is also examined by solving numerically the full set of fluid equations. The temporal behaviour of positive (compressive) solitary waves is found to be typical, i.e., the positive initial disturbance breaks up into a series of solitary waves with the largest in front. However, the behaviour of negative (rarefactive) solitary waves is quite different. These waves appear to be unstable and produce positive solitary waves at a later time. The relevancy of this investigation to observations in the magnetosphere of density depressions is briefly pointed out. Received 12 October 1999