Several envelope soliton fine structures have been observed in solar radio metric-wave emission.present a model of longitudinal modulational instability to explain these fine structures.It is found that this instabili...Several envelope soliton fine structures have been observed in solar radio metric-wave emission.present a model of longitudinal modulational instability to explain these fine structures.It is found that this instability can only occur in the condition of sound velocity being larger than Alfvin velocity in corona.Therefore,the envelope soliton fine structures should display in the coronal region with high temperature and low magnetic 6eld,which corresponds to the solar radio emission in the region of meter and decameter wavelength.展开更多
In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist ...In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solirons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j0.展开更多
The reductive perturbation method of multiple-scales is used to investigate the weak nonlinear modulation of the stress wave on the wall of a fluid-filled elastic circular tube. In the case of a single mode, the nonli...The reductive perturbation method of multiple-scales is used to investigate the weak nonlinear modulation of the stress wave on the wall of a fluid-filled elastic circular tube. In the case of a single mode, the nonlinear Schrodinger equation which the wave amplitude satisfies and its envelope soliton solution of stress wave are obtained.展开更多
We study an intense beam propagating through the double periodic focusing channel by the particle-coremodel,and obtain the beam envelope equation.According to the Poincare-Lyapunov theorem,we analyze the stabilityof b...We study an intense beam propagating through the double periodic focusing channel by the particle-coremodel,and obtain the beam envelope equation.According to the Poincare-Lyapunov theorem,we analyze the stabilityof beam envelope equation and find the beam halo.The soliton control method for controlling the beam halo-chaos isput forward based on mechanism of halo formation and strategy of controlling beam halo-chaos,and we also prove thevalidity of the control method,and furthermore,the feasible experimental project is given.We perform multiparticlesimulation to control the halo by using the soliton controller.It is shown that our control method is effective.We alsofind the radial ion density changes when the ion beam is in the channel,not only the halo-chaos and its regeneration canbe eliminated by using the nonlinear control method,but also the density uniformity can be found at beam's centre aslong as an appropriate control method is chosen.展开更多
We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand da...We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand damping to the set of deterministic motion equations.We define'half-time'as the time when the amplitude of theenvelope soliton decreases by half due to damping.And then the mass,center and half-time of the perturbed envelopesoliton are numerically simulated,beginning with the discrete envelope soliton at rest.Results show successfully hownoise affects behavior of the envelope soliton.展开更多
In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in line...In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.展开更多
A parametrically excited higher-order nonlinear Schrodinger (NLS) equation is derived to describe the interaction of a,slowly moving planetary-scale envelope Rossby soliton for zonal wavenumber-two with a wavenumber-t...A parametrically excited higher-order nonlinear Schrodinger (NLS) equation is derived to describe the interaction of a,slowly moving planetary-scale envelope Rossby soliton for zonal wavenumber-two with a wavenumber-two topography under the LG-type dipole near-resonant condition. The numerical solution of this equation is made. It is found that in a weak background westerly wind satisfying the LG-type dipole near-resonance condition, when an incipient envelope Rossby soliton is located in the topographic trough and propagates slowly, it can be amplified though the near-resonant forcing of wavenumber-two topography and can exhibit an oscillation. However, this soliton can break up after a long the and excite a train of small amplitude waves that propagate west ward. In addition, it is observed that in the soliton-topography interaction the topographically near-resonantly forced planetary-scale soliton has a slowly westward propagation, but a slowly eastward propagation after a certain time. The instantaneous total streamfunction fields of the topographically forced planetary-scale soliton are found to bear remarkable resemblance to the initiation, maintenance and boy of observed mega-type blocking high and dipole blocking. The soliton perturbation theory is used to examine the role of a wavenumber-two topography in near-resonantly forcing omega-type blocking high and dipole blocking. It can be shown that in the amplifying process of forced planetary-scale soliton, due to the inclusion of the higher order terms its group velocity gradually tends to be equal to its phase velocity so that the block envelope and carrier wave can be phase-locked at a certain time. This shows that the initiation of blocking is a transfer of amplified envelope soliton system from dispersion to nondispersion. However, there exists a reverse process during the decay of blocking. It appears that in the higher latitude regions, the planetary-scale envelope soliton-topography interaction could be regarded as a possible mechanism of the esta展开更多
A variable coefficient Korteweg de Vries （VCKdV） system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical ...A variable coefficient Korteweg de Vries （VCKdV） system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical solution obtained from the VCKdV equation can be successfully used to explain fruitful phenomena in fluid and other physical fields, for instance, the atmospheric blocking phenomena. In particular, a diploe blocking case happened during 9 April 1973 to 18 April 1973 read out from the National Center for Environmental Prediction/National Center for Atmospheric Research （NCEP/NCAR） reanalysis data is well described by the analytical solution.展开更多
In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the de...In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （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 Schrodinger 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.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.19803050.
文摘Several envelope soliton fine structures have been observed in solar radio metric-wave emission.present a model of longitudinal modulational instability to explain these fine structures.It is found that this instability can only occur in the condition of sound velocity being larger than Alfvin velocity in corona.Therefore,the envelope soliton fine structures should display in the coronal region with high temperature and low magnetic 6eld,which corresponds to the solar radio emission in the region of meter and decameter wavelength.
基金The project supported by the Natural Science Foundation of Hunan Province of China under Grant No. 03JJY6008
文摘In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solirons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j0.
基金The Project Supported by National Science Foundation of China
文摘The reductive perturbation method of multiple-scales is used to investigate the weak nonlinear modulation of the stress wave on the wall of a fluid-filled elastic circular tube. In the case of a single mode, the nonlinear Schrodinger equation which the wave amplitude satisfies and its envelope soliton solution of stress wave are obtained.
基金National Natural Science Foundation of China under Grant Nos.10247005 and 70071047the Scientific Research Foundation of China University of Mining and Technology for the Young Teachers under Grant No.OK060119
文摘We study an intense beam propagating through the double periodic focusing channel by the particle-coremodel,and obtain the beam envelope equation.According to the Poincare-Lyapunov theorem,we analyze the stabilityof beam envelope equation and find the beam halo.The soliton control method for controlling the beam halo-chaos isput forward based on mechanism of halo formation and strategy of controlling beam halo-chaos,and we also prove thevalidity of the control method,and furthermore,the feasible experimental project is given.We perform multiparticlesimulation to control the halo by using the soliton controller.It is shown that our control method is effective.We alsofind the radial ion density changes when the ion beam is in the channel,not only the halo-chaos and its regeneration canbe eliminated by using the nonlinear control method,but also the density uniformity can be found at beam's centre aslong as an appropriate control method is chosen.
基金Supported by Scientific Research Fund of Hunan Provincial Education Department under Grant No.07B075Interactive Project Fund of Xiangtan University under Grant No.061ND09Initial Scientific Research Fund of Xiangtan University
文摘We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand damping to the set of deterministic motion equations.We define'half-time'as the time when the amplitude of theenvelope soliton decreases by half due to damping.And then the mass,center and half-time of the perturbed envelopesoliton are numerically simulated,beginning with the discrete envelope soliton at rest.Results show successfully hownoise affects behavior of the envelope soliton.
基金Supported by National Natural Science Foundation of China under Grant No.90511009
文摘In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.
基金This study was supported jointly by the Foundation for University Key Teacher by the Ministry of Education, the National Natural
文摘A parametrically excited higher-order nonlinear Schrodinger (NLS) equation is derived to describe the interaction of a,slowly moving planetary-scale envelope Rossby soliton for zonal wavenumber-two with a wavenumber-two topography under the LG-type dipole near-resonant condition. The numerical solution of this equation is made. It is found that in a weak background westerly wind satisfying the LG-type dipole near-resonance condition, when an incipient envelope Rossby soliton is located in the topographic trough and propagates slowly, it can be amplified though the near-resonant forcing of wavenumber-two topography and can exhibit an oscillation. However, this soliton can break up after a long the and excite a train of small amplitude waves that propagate west ward. In addition, it is observed that in the soliton-topography interaction the topographically near-resonantly forced planetary-scale soliton has a slowly westward propagation, but a slowly eastward propagation after a certain time. The instantaneous total streamfunction fields of the topographically forced planetary-scale soliton are found to bear remarkable resemblance to the initiation, maintenance and boy of observed mega-type blocking high and dipole blocking. The soliton perturbation theory is used to examine the role of a wavenumber-two topography in near-resonantly forcing omega-type blocking high and dipole blocking. It can be shown that in the amplifying process of forced planetary-scale soliton, due to the inclusion of the higher order terms its group velocity gradually tends to be equal to its phase velocity so that the block envelope and carrier wave can be phase-locked at a certain time. This shows that the initiation of blocking is a transfer of amplified envelope soliton system from dispersion to nondispersion. However, there exists a reverse process during the decay of blocking. It appears that in the higher latitude regions, the planetary-scale envelope soliton-topography interaction could be regarded as a possible mechanism of the esta
基金Supported by the National Natural Science Foundation of China under Grant Nos 90203001, 10475055, 10547124 and 40305009.
文摘A variable coefficient Korteweg de Vries （VCKdV） system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical solution obtained from the VCKdV equation can be successfully used to explain fruitful phenomena in fluid and other physical fields, for instance, the atmospheric blocking phenomena. In particular, a diploe blocking case happened during 9 April 1973 to 18 April 1973 read out from the National Center for Environmental Prediction/National Center for Atmospheric Research （NCEP/NCAR） reanalysis data is well described by the analytical solution.
基金supported by the National Natural Science Foundation of China(Grant No.41406018)
文摘In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （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 Schrodinger 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.
