中心对称光折变材料中的小光强空间孤子

给出了小光强条件下中心对称光折变材料中光波演化方程的亮、暗及灰空间孤子解析解，并推导出了孤子宽度的显式表达式． 关键词： 光折变效应 光折变材料 空间孤子     

Time-Dependent Gaussian Solution for the Kostin Equation Around Classical Trajectories

The structure of time-dependent Gaussian solutions for the Kostin equation in dissipative quantum mechanics is analyzed. Expanding the generic external potential near the center of mass of the wave packet, one conclude that: the center of mass follows the dynamics of a classical particle under the external potential and a damping proportional to the velocity; the width of the wave packet satisfy a non-conservative Pinney equation. An appropriate perturbation theory is developed for the free particle case, solving the long standing problem of finding analytic expressions for square integrable solutions of the free Kostin equation. The associated Wigner function is also studied.     

Traveling-waves and solitons in a generalized time-variable coefficients nonlinear Schrödinger equation with higher-order terms

In this work, we study exact solutions of a generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with higher-order terms, and the dispersion and the nonlinear coefficients engendering temporal dependency. Similarity transformations are used to convert the nonautonomous equation into autonomous one and then we present solutions in a general way. These solutions are obtained for the first class by using the F-expansion method and for the second class constituted by most general bright, dark and front by a direct substitution. We also generalize the external potential which traps the system and the nonlinearities. Finally, the stability of the soliton solutions under slight disturbance of the constraint conditions and initial perturbation of white noise is discussed analytically and numerically. The results reveal that solitons can propagate in a stable way under slight disturbance of the constraint conditions and initial perturbation of a 10% white noise.     

Solitary Wave Dynamics in an External Potential

We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We consider solutions of the equations with a non-vanishing external potential corresponding to initial conditions close to one of these solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newtons equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping.Supported by NSERC grant 22R80976The support of Wenner-Gren Foundation is gratefully acknowledgedSupported partially by NSERC under NA7601 and by NSF under DMS-0400526Acknowledgement. B.L.G.J. and I.M.S. are grateful to J. Colliander for useful discussions and remarks and to ETH-Zürich for hospitality during their work on this paper. J.F. thanks T.-P. Tsai and H.-T. Yau for very useful discussions and correspondence which led to the results in [16,17].     

Third order susceptibility enhancement using GaN based composite nanoparticle

In this work, we are going to introduce a new composite nanostructure (metal-dielectric) based on GaN to manage optical and electrical properties. For doing and evaluation of these properties, first, we evaluated and calculated the wave functions and energy levels of the introduced structure by solving the Schrodinger equation analytically. Then using wave function nonlinear optical properties such as third order susceptibility are studied. We observed that with control of nanoparticle parameters different behavior is obtained. For example with increase of the well width, third order susceptibility is decreased too but with more increasing the well width we observed increasing the nonlinear susceptibility. This effect depends on different displacement of ground and first excited stated energy levels and consequently wave functions due to changing of defect radius. Also, we show that the third order susceptibility in this case is very larger than bulk cases. Finally it should mention that the reported results are for wavelengths larger than 30 μm.     

Evolution of the exact spatiotemporal periodic wave and soliton solutions of the (3 + 1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients

In this paper the spatiotemporal evolution of the periodic wave is investigated analytically when the laser passes through the inhomogeneous nonlinear medium. Firstly, the (3 + 1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients is solved analytically by an improved homogeneous balance principle and F-expansion technique. A number of exact periodic traveling wave and spatiotemporal soliton solutions are obtained. Then, their propagation characteristics are analyzed in detail. It is found that the evolutions of propagation of spatiotemporal soliton and periodic wave solutions are regular when the diffraction and dispersion coefficients are the identical distributed coefficients, but the evolutions of propagation of these solutions are irregular with other coefficients.     

Bifurcations and chaos in a parametrically damped two-well Duffing oscillator subjected to symmetric periodic pulses

We study a parametrically damped two-well Duffing oscillator, subjected to a periodic string of symmetric pulses. The order-chaos threshold when altering solely the width of the pulses is investigated theoretically through Melnikov analysis. We show analytically and numerically that most of the results appear independent of the particular wave form of the pulses provided that the transmitted impulse is the same. By using this property, the stability boundaries of the stationary solutions are determined to first approximation by means of an elliptic harmonic balance method. Finally, the bifurcation behavior at the stability boundaries is determined numerically.     

Mechanical stresses in an irradiated target with a disturbed surface

Mechanical stresses generated in a disturbed-surface solid target irradiated by intense fluxes of accelerated charged particles are studied numerically and analytically. The disturbed surface is needed to analyze the influence of microirregularities present on real surfaces on the stress pattern. Three basic components of the stress field are revealed: a shock wave; stresses localized in the energy liberation region; and disturbed stresses, which are due to the disturbed surface. The disturbed stresses are localized in a surface layer of width comparable to the disturbance wavelength and account for about 30% of the field stress energy. It is concluded that the disturbance of the surface and disturbance-induced stresses should be taken into account in analysis of structural transformations under irradiation.     

Non-autonomous bright matter wave solitons in spinor Bose–Einstein condensates

We investigate the dynamics of bright matter wave solitons in spin-1 Bose–Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross–Pitaevskii (3-GP) equations using Hirota?s method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite–Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.     

Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrdinger equation analytically by performing the Hirota's bilinearization method. The precise expression of a parameter , which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton (∈2≠1) while it has no effects on the wave central position.Moreover, the precise expressions of a nonautonomous black soliton's (∈2≠1) width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton's evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.     

光折变有机聚合物中的空间孤子

给出了稳态情况下光折变聚合物中光波演化方程的亮、暗及灰孤子解,并讨论了不同孤子态的偏振特性及孤子宽度与外加电场的关系. 关键词： 光折变 聚合物 空间孤子     

Soliton dynamics and elastic collisions in a spin chain with an external time-dependent magnetic field

In this paper, we investigate the nonlinear dynamics of a Heisenberg spin chain with an external time-oscillating magnetic field. Such dynamics can be described by a Landau–Lifshitz-type equation. We apply the Darboux transformation method to the linear eigenvalue problem associated with this equation, and obtain the multi-soliton solution with a purely algebraic iterative procedure. Through the analytical analysis and graphical illustrations for the solutions obtained, we discuss in detail the effects of an external magnetic field on the nonlinear wave. Under the action of an external field, although the amplitude, width and depth of soliton vary periodically with time and its symmetry property is changeable, the soliton can also propagate stably and it possesses particle-like behavior.     

Non-autonomous wave solutions for the Gross-Pitaevskii (GP) equation with a parabola external potential in Bose-Einstein condensates

A Gross-Pitaevskii (GP) equation with a parabola external potential is considered, and is transformed into a standard nonlinear Schrödinger (NLS) equation. By using the homogeneous balance principle and F-expansion method, we study non-autonomous wave solutions of the GP equation with a parabola external potential. In particular, based on the similarity transformation, several families of non-autonomous wave solutions of the GP equation are presented with snaking behaviors and different amplitude surfaces. These obtained bright-dark soliton solutions can give some potential applications in Bose-Einstein condensates.     

Analytical Periodic Wave and Soliton Solutions of the Generalized Nonautonomous Nonlinear Schrödinger Equation in Harmonic and Optical Lattice Potentials

We construct analytical periodic wave and soliton solutions to the generalized nonautonomous nonlinear Schrödinger equation with time- and space-dependent distributed coefficients in harmonic and optical lattice potentials. We utilize the similarity transformation technique to obtain these solutions. Constraints for the dispersion coefficient, the nonlinearity, and the gain (loss) coefficient are presented at the same time. Various shapes of periodic wave and soliton solutions are studied analytically and physically. Stability analysis of the solutions is discussed numerically.     

Small Amplitude Solitons in Bose--Einstein Condensates with External Perturbation

By developing a small amplitude soliton approximation method, we study analytically weak nonlinear excitations in cigar-shaped condensates with repulsive interatomic interaction under consideration of external perturbation potential. It is shown that matter wave solitons may exist and travel over a long distance without attenuation and change in shape by properly adjusting the strength of interatomic interaction to compensate for the effect of external perturbation potential.     

Consistent Riccati expansion solvability,symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves

We study a forced variable-coefficient extended Korteweg-de Vries (KdV) equation in fluid dynamics with respect to internal solitary wave. Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevé expansion. When the variable coefficients are time-periodic, the wave function evolves periodically over time. Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations. One-parameter group transformations and one-parameter subgroup invariant solutions are presented. Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method. The consistent Riccati expansion (CRE) solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE. Interaction phenomenon between cnoidal waves and solitary waves can be observed. Besides, the interaction waveform changes with the parameters. When the variable parameters are functions of time, the interaction waveform will be not regular and smooth.     

(3+1)-dimensional localized self-accelerating Airy elegant Ince-Gaussian wave packets and their radiation forces in free space

We construct analytically linear self-accelerating Airy elegant Ince–Gaussian wave packet solutions from(3+1)-dimensional potential-free Schr odinger equation. These wave packets have elliptical geometry and show different characteristics when the parameters(p, m) and ellipticity ε are adjusted. We investigate these characteristics both analytically and numerically and give the 3-dimensional intensity and phase distribution of these wave packets. Lastly, we analyze the radiation forces on a Rayleigh dielectric particle. In addition, we also find an interesting phenomenon that if the energy distribution between every part of wave packets is uneven at the input plane, the energy will be transferred between every part in the process of transmission.     

Analytical studies of two-component Bose-Einstein condensates in two-dimensional optical lattices

The two-component Bose-Einstein condensates (BECs) trapped in 2D optical lattice potential is studied analytically. A new family of stationary exact solutions of the coupled Gross-Pitaevskii (GP) equations with 2D periodic potential are obtained. In particular, the phase diagram of the system in the trigonometric limit is determined analytically according to the nontrivial phase macroscopic wave functions of the condensates.     

Analytic Results in the Position-Dependent Mass Schrödinger Problem

We investigate the Schrödinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V(x)=0 case whose solutions are hypergeometric functions in tanh²x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V(x)=V₀ sinh²x.     

Double hump solitary waves in quadratic media with walk-off – domain of existence,stability and decay scenarios

We analytically determine the domain of existence of double hump solitary wave solutions in quadratic media with walk-off. Although a linear stability analysis reveals that these solutions are always unstable the instability gain can be very small for certain parameters. This has important implications for all-optical switching applications. The ultimate decay is prompted by the destruction of an exact phase difference π between the two humps of the fundamental frequency wave and follows different scenarios.