Envelope Solitons Perturbed by Stochastic Noise

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.

Gray Envelope Solitons in Quantum Electron Plasmas

By using the traditional perturbation method, we obtain the nonlinear Sehrodinger equation for one-dimensional Schrodinger-Poisson system. Some of its solutions can explain previous results.

A Novel Envelope Soliton Solution to the Granular Crystal Model

A theoretical work on envelope solitons to a one-dimensional granular chain model is reported. In the small amplitude approximation, we analytically solve the equation of motion with the help of the semidiscrete multiple-scale method. Our results show that the granular chain model can support an asymmetric high-order envelope soliton under the certain condition. It is found that the second-harmonic term of this high-order envelope soliton has an additional phase. In addition, the influence of both the material parameter and the static load on the localized features of the high-order envelope soliton is discussed.

THE ENVELOPE SOLITON OF STRESS WAVE ON THE WALL OF A FLUID-FILLED CIRCULAR TUBE

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.

Interaction between a Slowly Moving Planetary-Scale Dipole Envelope Rossby Soliton and a Wavenumber-Two Topography in a Forced Higher Order Nonlinear Schr■dinger Equation

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 establishment of blocking.

Equatorial Envelope Rossby Solitions in a Shear Flow

A simple shallow-water model on an equatorial β-plane is employed to investigate the nonlinear equatorial Rossby solitons in a mean zonal flow with meridional shear by the asymptotic method of multiple scales. The cubic nonlinear Schr?dinger (NLS, for short) equation, satisfied for large amplitude equatorial envelope Rossby solitons in shear basic flow, is derived. The effects of basic flow shear on the nonlinear equatorial Rossby solitons are also analyzed. Key words Envelope solitons - NLS This work was supported by the Foundation for University Key Teacher by the Ministry of Education.

Quantum Solitons and Localized Modes in a One-Dimensional Lattice Chain with Nonlinear Substrate Potential

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.

The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity

By virtue of the method of multiple-scale and the quasi-discreteness approach, we have discussed the nonlinear vibration equation of a 3D discrete monatomic lattice with its nearest-neighbours interaction. The 3D simple cubic lattices have the same localized modes as a 1D discrete monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop solitons in the direction of kx = ky = kz = k and k = ±π/6α0 in the Brillouin zone, as well as has 3D vortices in the direction of kx = ky = kz = k and k = ±π/α0 in the Brillouin zone.