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1.
Nonlinear theory of electrostatic baryonic waves in ambiplasma 总被引:1,自引:0,他引:1
A. E. Dubinov S. K. Saikov A. P. Tsatskin 《Journal of Experimental and Theoretical Physics》2011,112(6):1051-1060
A collisionless nonmagnetized ambiplasma consisting of Maxwellian gases of protons, antiprotons, electrons, and positrons
is considered. The dispersion relation for electrostatic baryonic waves is derived and analyzed and exact expressions for
the linear wave phase velocities are obtained. Two types of such waves are shown to be possible in ambiplasma: acoustic and
plasma ones. Analysis of the dispersion relation has allowed the ranges of parameters in which nonlinear solutions should
be sought in the form of solitons to be found. A nonlinear theory of baryonic waves is developed and used to obtain and analyze
the exact solution to the basic equations. The analysis is performed by the method of a fictitious potential. The ranges of
phase velocities of periodic baryonic waves and soliton velocities (Mach numbers) are determined. It is shown that in the
plasma under consideration, these ranges do not overlap and that the soliton velocity cannot be lower than the linear velocity
of the corresponding wave. The profiles of physical quantities in a periodic wave and a soliton (wave scores) are plotted. 相似文献
2.
A collisionless nonmagnetized e-p-i plasma consisting of quantum-degenerate gases of ions, electrons, and positrons at nonzero temperatures is considered. The
dispersion equation for isothermal ionic sound waves is derived and analyzed, and an exact expression is obtained for the
linear velocity of ionic sound. Analysis of the dispersion equation has made it possible to determine the ranges of parameters
in which nonlinear solutions in the form of solitons should be sought. A nonlinear theory of isothermal ionic sound waves
is developed and used for obtaining and analyzing the exact solution to the system of initial equations. Analysis has been
carried out by the method of the Bernoulli pseudopotential. The ranges of phase velocities of periodic ionic sound waves and
soliton velocities are determined. It is shown that in the plasma under investigation, these ranges do not overlap and that
the soliton velocity cannot be lower than the linear velocity of ionic sound. The profiles of physical quantities in a periodic
wave and in a soliton are constructed, as well as the dependences of the velocity of sound and the critical velocity on the
ionic concentration in the plasma. It is shown that these velocities increase with the ion concentration. 相似文献
3.
基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象.
关键词:
浅水波方程
大尺度正压大气
解析解
非线性波 相似文献
4.
A nonlinear theory of propagating periodic and nonlinear solitary waves (like kinks and solitons) related to the motion of
defects in crystals and of specific periodic waves into which the former ones transform in the field of the compression stress
was developed. The role of intense tension stress leading to the heavy structural rearrangement of the crystal as a result
of the effect of the external stress on the interatomic potential barriers was taken into account as well. Crystals with a
complex lattice consisting of two sublattices were considered. Arbitrarily large displacements of sublattices were analyzed.
The nonlinear theory is based on an additional element of the translational symmetry typical for complex lattices but not
introduced earlier in solid-state physics. The variational equations of macroscopic and microscopic displacements turn out
to be a nonlinear generalization of the linear equations of acoustic and optical modes obtained by Carman, Born, and Huang
Kun. The microscopic displacement fields are described by the nonlinear sine-Gordon equation. In the one-dimensional case,
exact solutions of the nonlinear equations were found and their features were revealed. In the case of two-dimensional (2+1)
fields, new methods of the exact solutions of the sine-Gordon equation were developed. They describe the interaction of the
nonlinear waves with the structural inhomogeneities of solid state due to the external fields of stress and deformations. 相似文献
5.
We present a complete theoretical analysis of the periodic and non-periodic travelling waves in a diatomic chain model, in
the continuum limit by incorporating nonlinear sixth order polarization potential (φ6) at the anion site. We have formulated a nonlinear lattice dynamical theory in which various energy curves are obtained for
different types and magnitudes of the core-shell force constants. For periodic solutions, we have obtained two types of commensurate
wave amplitudes which propagate in the opposite direction with respect to each other. For nonperiodic solutions, we have obtained
various travelling excitations such as kink, antikink, excitons etc. for different values of the mass ratio and velocity parameter.
The dipole moment per unit charge for SrTiO3 has been calculated and it is found that the nonlinear excitations in this model carry large amount of energy as compared
to those obtained from harmonic and anharmonic optical phonons in the φ4-polarizable model. 相似文献
6.
7.
《Physics Reports》1997,286(4):199-270
A new method of finding the periodic solutions for the equations integrable within the framework of the AKNS scheme is reviewed. The approach is a modification of the known finite-band integration method, based on the re-parametrization of the solution with the use of algebraic resolvent of the polynomial defining the solution in the finite-band integration method. This approach permits one to obtain periodic solutions in an effective form necessary for applications. The periodic solutions are found for such systems as the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation, the Heisenberg model, the uniaxial ferromagnet, the AB system, and self-induced transparency and stimulated Raman scattering equations. The modulation Whitham theory describing the slow modulation of periodic waves is expressed in a form convenient for applications. The Whitham equations are obtained for all abovementioned cases. The technique developed is applied to the nonlinear theory of modulational instability describing the transformation of a local disturbance expanding into a nonuniform region presented as a modulated periodic wave whose evolution is governed by the Whitham equations. This theory explains the formation of solitons on the sharp front of a long pulse. 相似文献
8.
Nominally 2-dimensional viscous flow induced by gravity waves over a spatially periodic bed is simulated by a Lagrangian vortex scheme. A vortex sheet is introduced on the surface at each time step to satisfy the zero velocity conditions. The sheet is discretised; the vortex-in-cell method is used to convect vorticity and random walks are added to effect viscous diffusion. Good agreement with analytical theory is obtained for velocity profiles in uniform sinusoidal flow and for mass transport due to linear waves. Mass transport for finite amplitude waves is also obtained. For separated flow over rippled beds, which is still liminar, a vortex decay factor is required to produce agreement with experiment and is thought to compensate for large scale 3-dimensional effects. 相似文献
9.
Nonlinear Propagation of Positron-Acoustic Periodic Travelling Waves in a Magnetoplasma with Superthermal Electrons and Positrons 下载免费PDF全文
《中国物理快报》2017,(6)
The nonlinear propagation of positron acoustic periodic(PAP) travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ions is examined. The reductive perturbation technique is employed to derive a nonlinear Zakharov-Kuznetsov equation that governs the essential features of nonlinear PAP travelling waves. Moreover, the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions. It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves. It is observed that the superthermality of hot positrons, the concentrations of superthermal electrons and positrons, the positron cyclotron frequency, the direction cosines of wave vector k along the z-axis,and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves. The present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons. 相似文献
10.
We have studied the influence of external static (pressure) and dynamic (caused by an elastic wave with a finite amplitude) actions on the linear and nonlinear elastic properties of a granulated unconsolidated medium, which was simulated by steel spheres with diameters of 2 and 4 mm. We have analyzed the equation of state for such a medium taking into account the presence of weakly and strongly deformed contacts between individual spheres. We have obtained expressions for the elasticity coefficient and second- and third-order nonlinear elastic parameters, and we have experimentally studied the influence of external static pressure on their values. We have measured the dependence of the velocity of elastic waves on external static pressure and the probing signal amplitude. In the studied medium, a number of structural phase transitions were observed, related to rearrangement of the packing of spheres, which were caused by both static and dynamic actions. The structural phase transition was accompanied by an anomalous change in the nonlinear elastic parameters of the medium and the velocity of elastic waves. We have analyzed the results based on the Hertz theory of contact interaction. 相似文献
11.
12.
L. Yu Z.-K. Shi 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(1):115-120
The car-following model of traffic flow is extended to
take into account the relative velocity. The stability condition
of this model is obtained by using linear stability theory. It is
shown that the stability of uniform traffic flow is improved by
considering the relative velocity. From nonlinear analysis, it is
shown that three different density waves, that is, the triangular
shock wave, soliton wave and kink-antikink wave, appear in the
stable, metastable and unstable regions of traffic flow
respectively. The three different density waves are described by
the nonlinear wave equations: the Burgers equation, Korteweg-de
Vries (KdV) equation and modified Korteweg-de Vries (mKdV)
equation, respectively. 相似文献
13.
O. V. Rudenko 《Radiophysics and Quantum Electronics》2003,46(5-6):338-351
We briefly review the effects of nonlinear self-action of beams of strongly distorted waves containing steep shock fronts. The features of inertial self-actions of periodic sawtooth waves in quadratic nonlinear media without dispersion are discussed. These phenomena can be caused by an acoustic wind or thermal lens formed as a result of the nonlinear dissipation at the shock fronts. Instantaneous self-actions are analyzed on the examples of periodic trapezoidal waves, which are formed in cubic nonlinear media and contain alternating compression and rarefaction shocks, and a single-pulse signal containing a shock front. Mathematical models and solutions to the corresponding nonlinear equations are given. A qualitative comparison with optical self-action phenomena and with available experimental data is performed. 相似文献
14.
Rogue Waves in the (2+1)-Dimensional Nonlinear Schrodinger Equation with a Parity-Time-Symmetric Potential 下载免费PDF全文
《中国物理快报》2017,(1)
The(2+1)-dimension nonlocal nonlinear Schrodinger(NLS) equation with the self-induced parity-time symmetric potential is introduced, which provides spatially two-dimensional analogues of the nonlocal NLS equation introduced by Ablowitz et al. [Phys. Rev. Lett. 110(2013) 064105]. General periodic solutions are derived by the bilinear method. These periodic solutions behave as growing and decaying periodic line waves arising from the constant background and decaying back to the constant background again. By taking long wave limits of the obtained periodic solutions, rogue waves are obtained. It is also shown that these line rogue waves arise from the constant background with a line profile and disappear into the constant background again in the(x,y) plane. 相似文献
15.
《Physics letters. A》1998,249(4):315-323
Weakly nonlinear magneto-acoustic waves propagating at an arbitrary angle to the external magnetic field in a rotating plasma are considered. A model equation (Ostrovsky's equation with positive dispersion) is derived from a set of basic magneto-hydrodynamic equations. Stationary solutions of this equation are obtained numerically and analyzed in detail theoretically. These include solitary-type solutions (solitons with monotonic and oscillating tails), complex multisolitons (bound states of coupled single solitons), as well as periodic waves. We emphasize that the positive dispersion, in contrast to the negative one, gives rise to solitary waves within the framework of Ostrovsky's equation. 相似文献
16.
Jared Bronski Mathew A. Johnson Todd Kapitula 《Communications in Mathematical Physics》2014,327(2):521-550
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the “good” Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the “good” Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg–de Vries equation. 相似文献
17.
Nonlinear waves on periodic backgrounds play an important role in physical systems. In this study, nonlinear waves that include solitons, breathers, rogue waves, and semi-rational solutions on periodic backgrounds for the coupled Lakshmanan-Porsezian-Daniel equations are investigated. Moreover, the interactions between different types of nonlinear waves are examined and their dynamic behaviors are studied. In particular, it is observed that bright-dark rogue waves interact with bright-dark breathers or solitons on periodic backgrounds, four-petaled breathers interact with two eye-shaped breathers on periodic backgrounds, and a four-petal rogue wave interplays with a rogue wave on periodic backgrounds. Furthermore, it is found that the value of the parameter γ3 affects the weak and strong interactions of these nonlinear waves. These results may be useful in the study of nonlinear wave dynamics in coupled nonlinear wave models. 相似文献
18.
Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere 下载免费PDF全文
Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations
with a higher-degree of nonlinear terms are derived from a simple
incompressible non-hydrostatic Boussinesq equation set in atmosphere
and are used to investigate gravity waves in atmosphere. By taking
advantage of the auxiliary nonlinear ordinary differential equation,
periodic wave and solitary wave solutions of the fifth-order
KdV--mKdV models with higher-degree nonlinear terms are obtained
under some constraint conditions. The analysis shows that the
propagation and the periodic structures of gravity waves depend on
the properties of the slope of line of constant phase and atmospheric
stability. The Jacobi elliptic function wave and solitary wave
solutions with slowly varying amplitude are transformed into
triangular waves with the abruptly varying amplitude and breaking
gravity waves under the effect of atmospheric instability. 相似文献
19.
Periodic Structure of Equatorial Envelope Rossby Wave Under
Influence of Diabatic Heating 总被引:1,自引:0,他引:1
FUZun-Tao CHENZhe LIUShi-Da LIUShi-Kuo 《理论物理通讯》2004,42(1):43-48
A simple shallow-water model with influence of diabatic heating on a β-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schro^edinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacob/elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form. 相似文献
20.
MA Chunsheng 《Chinese Journal of Lasers》1998,7(6):523-528
1IntroductionNonlinearmultilayerstructuresincludingnonlinearmultiplequantumwelsystemsposessomedistinctivefeaturesasstrongerop... 相似文献