共查询到20条相似文献,搜索用时 15 毫秒
1.
《Journal of Nonlinear Mathematical Physics》2013,20(3-4):391-395
Abstract The infinite series of Lorentz and Poincaré-invariant nonlinear versions of the Maxwell equations are suggested. Some properties of these equations are considered. 相似文献
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LI Hua-Mei 《理论物理通讯》2009,51(2):279-282
This paper analyzes spatial grey self-similar solitary waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities. New exact self-similar solutions are found using a novel transformation and their main features are investigated by using direct computer simulations. 相似文献
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ZHONG Wei-Ping YI Lin YANG Zheng-Ping XIE Rui-Hua BELI Milivoj CHEN Goong 《理论物理通讯》2008,50(3):749-752
Collisions of spatial solitons occurring in the nonlinear
Schröinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium
when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no
transmission of stable spatial solitons is possible. However, in such media
the linear focusing effect can be exactly compensated, and the spatial
solitons can propagate through. 相似文献
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ZHONG Wei-Ping YI Lin YANG Zheng-Ping XIE Rui-Hua BELIC Milivoj CHEN Goong 《理论物理通讯》2008,50(9):749-752
Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through. 相似文献
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In this paper, by solving a complex nonlinear Schr¨odinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain.Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate. 相似文献
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Jaros?aw Zale?ny 《International Journal of Theoretical Physics》2009,48(6):1801-1812
Maxwell equations in a resting and nonrelativisticly moving medium can be rewritten in a form of the Dirac equation. In the
paper the formal analogy between an electron in the electromagnetic field and a photon in the dielectric medium has been used
to consider three effects: Fresnel’s drag, mechanical Faraday effect (interpreted here as a procession of the photon spin)
and Landau frequencies in a rotating medium. The third effect, up to my knowledge, is new. It predicts that only some discrete
frequencies of light can propagate in a rotating medium. 相似文献
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XUE Yu-Shan TIAN Bo ZHANG Hai-Qiang LIU Wen-Jun LI Li-Li QI Feng-Hua ZHAN Yan 《理论物理通讯》2009,(11):888-896
With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e. Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers. 相似文献
10.
O. V. Rudenko 《Acoustical Physics》2018,64(4):422-431
The phenomenon of “wave resonance” which occurs at excitation of traveling waves in dissipative media possessing modular, quadratic and quadratically-cubic nonlinearities is studied. The mathematical model of this phenomenon is the inhomogeneous (or “forced”) equation of Burgers type. Such nonlinearities are of interest because the corresponding equations admit exact linearization and describe real physical objects. The presence of “accompanying sources” (traveling with the wave) on the right-hand side of the inhomogeneous equations ensures the inflow of energy into the wave, which thereafter spreads throughout the wave profile, flows to emerging shock fronts, and then dissipates due to linear and nonlinear losses. As an introduction, the phenomenon of wave resonance in ideal and dissipative media is described and physical examples are given. Exact expressions for nonlinear steady-state wave profiles are derived. Non-stationary processes of wave generation, spatial “beating” of amplitudes with different relationship between the speed of motion of the sources and the natural wave velocity in the medium are studied. Resonance curves are constructed that contain a nonlinear shift of the absolute maxima to the “supersonic” region. The features of the resonance in each of the three types of nonlinearity are discussed. 相似文献
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Gi-Ren Liu 《Journal of statistical physics》2015,158(5):1126-1146
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Maxwell equations are explicitly written in spin weighted form by using NP formalism in general flat spacetimes. Corresponding Maxwell equations are obtained in spinning and straight cosmic string backgrounds. 相似文献
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LIU Cheng-Shi 《理论物理通讯》2006,45(2):219-223
A trial equation method to nonlinear evolution equation
with rank inhomogeneous is given. As applications, the exact
traveling wave solutions to some higher-order nonlinear equations
such as generalized Boussinesq equation, generalized Pochhammer-Chree
equation, KdV-Burgers equation, and KS equation and so on, are
obtained. Among these, some results are new. The proposed method is
based on the idea of reduction of the order of ODE. Some mathematical
details of the proposed method are discussed. 相似文献
14.
Bendong Lou 《Journal of statistical physics》2007,129(3):509-516
We study convection-reaction-diffusion equations which have spatially inhomogeneous steady states. When the coefficients of
the reaction terms are much larger than the diffusion coefficients, sharp interfaces appear between two stable inhomogeneous
steady states. By using the method of matched asymptotic expansions, we derive the equations of the motion of such interfaces,
which depend on the mean curvature of the interfaces and depend on the inhomogeneous coefficients locally.
This work is partially supported by NNSF of China and SRF for ROCS, SEM (China). 相似文献
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Radiophysics and Quantum Electronics - We propose rheological models of micro- and structurally inhomogeneous media, which explain an increase in their acoustic nonlinearity with increasing wave... 相似文献
16.
非均匀平板波导的色散方程 总被引:6,自引:6,他引:0
利用转移矩阵理论分析了任意折射率分布平板波导的传输特性,导出了非均匀平板波导的近似解析色散方程,并指出了WKB近似的局限性,数值比较的结果表明,文中所得公式的精确度优于传统的WKB方法和其它近似方法。 相似文献
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S. E. Savotchenko 《JETP Letters》2018,107(8):455-457
A model of a planar defect with nonlinear properties, which separates media with a Kerr-type nonlinearity, has been considered. It has been found that new steady states appear in a medium with self-focusing because of the nonlinearity of the defect, which do not occur in the case of a linear defect. The energies of such states have been obtained in an analytical form. The conditions for existence of such states have been determined depending on the characteristics of the defect and medium. 相似文献
20.
S. E. Savotchenko 《Journal of Experimental and Theoretical Physics》2018,127(3):437-447
Spatially periodic inhomogeneous stationary states are shown to exist near a thin defect layer with nonlinear properties separating nonlinear Kerr-type crystals. The contacts of nonlinear self-focusing and defocusing crystals have been analyzed. The spatial field distribution obeys a time-independent nonlinear Schrödinger equation with a nonlinear (relative to the field) potential modeling the thin defect layer with nonlinear properties. Both symmetric and asymmetric states relative to the defect plane are shown to exist. It has been established that new states emerge in a self-focusing crystal, whose existence is attributable to the defect nonlinearity and which do not emerge in the case of a linear defect. The dispersion relations defining the energy of spatially periodic inhomogeneous stationary states have been derived. The expressions for the energies of such states have been derived in an explicit analytical form in special cases. The conditions for the existence of periodic states and their localization, depending on the defect and medium characteristics, have been determined. 相似文献