共查询到20条相似文献，搜索用时 31 毫秒
1.
The weakly nonlinear standing waves on the surface of a self-gravitating incompressible fluid column are investigated in the presence of, a uniform axial-magnetic field. By use of the method of multiple scales, we have shown that near the critical wave number, the amplitude modulation of a standing wave can be described by a nonlinear Schrödinger equation with the roles of time and space variable interchanged. It is demonstrated that in presence of a magnetic field, the system is always stable near the critical wave number.Department of Chemical Engineering, and TechnologyDepartment of Mathematics 相似文献
2.
S. K. El-Labany 《Astrophysics and Space Science》1991,182(2):241-247
The multiple scales perturbation theory is applied to a system of dispersive waves including plasma waves (ion-acoustic waves). Assuming the amplitudes of waves are slowly varying function of space and time, we find that long-time slow modulation of the complex amplitude can be described by the non-linear Schrödinger equation. This result agrees with that obtained by Shimizu and Ichikawa using the reductive perturbation theory, and agrees exactly with the nonrelativistic limit of the nonlinear Schrödinger equation obtained by Nejoh using the stretching method. 相似文献
3.
The Rayleigh-Taylor instability in hydromagnetics is investigated with the use of the method of multiple scales. It is shown that when the wavenumberK is equal to the critical wavenumberK c , the amplitude modulation of a standing wave can be described by the nonlinear Schrödinger equation from which the nonlinear cutoff wavenumber is subsequently derived. 相似文献
4.
In studying the nonlinear electrohydrodynamic stability of solitary wave packets of capillary-gravity waves, in (2+1) dimensions, for dielectric fluids, we found that the complex amplitude of the surface elevation can be described by a nonlinear Schrödinger equation which can be written in the form of a soliton envelope equation. Using the tanh method we get in a very simple way the solitary wave solutions of this equation which we had obtained before by using the Jacobian elliptic functions. 相似文献
5.
The evolution of two dimensional wave packets on the surface of a self-gravitating fluid layer is investigated and shown to be governed by a nonlinear Schrödinger equation. The wave train of finite amplitude is modulationally unstable. Obtained also are the dynamical equations for the second harmonic resonance. The analysis reveals that the general motion consists of both amplitude and phase modulated waves of which the pure phase and amplitude modulated waves, solitary waves, and phase jump are just the special cases. 相似文献
6.
P. K. Shukla 《Astrophysics and Space Science》1985,114(2):381-385
A nonlinear Schrödinger equation is obtained for linearly polarized electromagnetic waves propagating across the ambient magnetic field in an electron-positron plasma. The nonlinearities arising from wave intensity induced particle mass modulation, as well as harmonic generation are incorporated. Modulational instability and localization of pulsar radiation are investigated. 相似文献
7.
The effect of a uniform axial magenetic field on the nonlinear instability of a self-gravitating infinite cylinder is examined. Using the method of multiple scales, it is found that while the nonlinear (modulational) instability cannot be completely suppressed, the presence of a magnetic field does increase the range of stable wave numbers. The evolution of the amplitude is governed by a non-linear Schrödinger equation which gives the criterion for modulational instability.Department of Chemical Engineering and Technology.Department of Mathematics. 相似文献
8.
A finite amplitude linearly polarized electromagnetic wave propagating in a relativistic plasma, is found to generate the longitudinal d.c. as well as the oscillating electric field at the second harmonic. In a plasma consisting of only electrons and positrons, these fields cannot be generated.The evolution of the electromagnetic waves is governed by the non-linear Schrödinger equation which shows that the electromagnetic solitons are always possible in ultra-relativistic plasmas (electron-ion or electron-positron) but in a plasma with relativistic electrons and nonrelativistic ions, these solitons exist only if 1(KT
e/meC2)<(2m
i/15me);m
e andm
i being the electron and ion mass andT
e the electron temperature. Both the d.c. electric field and the solitons provide a nonlinear mechanism for anomalous acceleration of the particles. This model has direct relevance to some plasma processes occurring in pulsars. 相似文献
9.
S. Barcza 《Astrophysics and Space Science》1979,66(2):287-307
The Schrödinger equation is solved if an electron moves in the field of chargesZ
1 andZ
2 which are fixed in space. The wave function is expanded in power series, the eigenvalues are given graphically and partly in tabular form. The asymptotic behaviour of the eigenvalues is discussed when the distance of the two fixed charges is small and large. Some consequences are drawn on hydrogen line broadening, shift andgrenzkontinua. Further utilization of the calculations is indicated. The mathematical appendix helps to clarify some technical details of the calculations. 相似文献
10.
A multiple sclaes perturbation theory has been applied to investigate the nonlinear behaviour of beam-plasma system near a marginally stable state in the presence of longitudinal magnetic field. The perturbation method leads to a nonlinear Schrödinger equation for the finite amplitude. The coefficients of this equation show that only if the beam is compressed isothermally can there exist a range of wavenumbers for which stabilization might occur. The stable region increases with the applied magnetic field. 相似文献
11.
B. Buti 《Astrophysics and Space Science》1978,55(1):85-92
A non-linear Schrödinger equation which characterizes the non-linear electrostatic waves in collisionless turbulent plasma is derived. Detailed analysis of this equation for the non-linear Langmuir waves is presented to show how the ion dynamics affects the envelope behaviour of these waves. Necessary condition for the existence of Langmuir envelope solitons is found to bek
2
D
2
(m/M);k being the characteristic wave number, D the electron Debye length andm andM the electron and the proton mass.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978. 相似文献
12.
The modulational instability of the weakly nonlinear longitudinal Langmuir as well as the transverse electromagnetic waves, propagation in the relativistic plasma without the static fields is described. The nonlinear Schrödinger equation taking account of the nonlinear Landau damping for these waves has been derived by means of the relativistic Vlasov and Maxwell equations. The plasma with the weakly relativistic temperature and that with an ultrarelativistic one has been investigated. In the first case, for the electron-proton plasma with the temperature more than 2.3 KeV we found the regional change of the wave numbers for which the soliton of two types, subsonic and supersonic, can exist. The soliton of the transverse waves can exist when the group velocity of the waves is between the thermal velocity of the electron and ion and the length of the linear waves is less than 2c/
pi
.In the second case the regions of the wave numbers, with the solitons of the Langmuir and transverse waves have been determined.The nonlinear waves in the electron-positron plasma and the waves with the phase velocity, which is about the light one, are also considered in the following paper. 相似文献
13.
John K. Lawrence 《Solar physics》1988,116(1):17-32
We have studied the modulational stability of a finite-amplitude fast sausage magnetosonic surface wave traveling along a thin magnetic slab in the solar photosphere (chromosphere). The equation governing the evolution of the fast-wave envelope modulated by a slow wave driven by the ponderomotive force proves to be the cubic nonlinear Schrödinger equation which in photospheric conditions admits only dark envelope soliton solutions. The possibility of the existence of such solitary waves in the solar atmosphere is discussed. 相似文献
14.
Nonlinear interaction of finite-amplitude Alfvén waves with non-resonant finite-frequency electrostatic and stationary electromagnetic perturbations is considered. This interaction is governed by a pair of coupled equations consisting of nonlinear Schrödinger equation for the Alfvén wave envelope and an equation for the plasma slow response that is driven by the ponderomotive force of the Alfvén wave packets. The modulational instability of a constant amplitude Alfvén pump is investigated and some new results for the growth rate of the instability are presented. It is found that a possible stationary state of the modulated Alfvén wave packets could lead to localized structures. The relevance of our investigation to the solar atmosphere is discussed. 相似文献
15.
John A. Adam 《Astrophysics and Space Science》1987,133(2):317-337
The reduced linearized equations of ideal magnetohydrodynamics which are highly nonlinear in the eigenvalue parameter, are linearized about a prescribed value of that parameter, enabling the equation to be expressed as a Schrödinger equation with piecewise uniform coefficients. Reflection and transmission coefficients are obtained using standard techniques, and in addition to the possibility of total transmission of an incident wave occurring (together with complex-valued resonance energies), the magnetic field introduces other total transmission energy levels which have no counterpart in the absence of a magnetic field. 相似文献
16.
Jonas Lundberg 《Solar physics》1994,154(2):215-230
The weakly nonlinear wave propagation of a slow sausage surface wave traveling along a magnetized slab with a thin nonuniform boundary layer is considered. The ideal incompressible MHD equations are used and the nonlinearities are assumed to be due to second harmonic generation. A nonlinear dispersion relation and the related nonlinear Schrödinger equation is derived. The existence of a continuous thin interface leads to sharply peaked field amplitudes due to resonant interaction with local Alfvén waves. It is shown that the nonlinear effects from processes within the thin layer are much more important than those from the main slab. Furthermore, the nonlinear interaction with local Alfvén waves yields a nonlinear damping rate of the wave that is much larger than the linear damping rate when the transition layer is sufficiently thin. 相似文献
17.
B. Buti 《Astrophysics and Space Science》1978,58(1):89-97
The non-linear Schrödinger equation, describing the non-linear Langmuir waves in a relativistic Vlasov plasma in a strong magnetic field, is derived. In the relativistic limit,KT>mc
2, this equation gives envelope solitons which are discussed from a point of view of their applications to pulsars. 相似文献
18.
The stability of modulation of ion-acoustic waves in a collisionless electron–positron–ion plasma with warm adiabatic ions is studied. Using the Krylov–Bogoliubov–Mitropolosky (KBM) perturbation technique a nonlinear Schrödinger equation governing the slow modulation of the wave amplitude is derived for the system. It is found that for given set of parameters having finite ion temperature ratio (T i /T e ) the waves are unstable for the values of k lying in the range k min<k<k max. On increasing the ion temperature ratio (T i /T e ), it is found that k min and k max, both decreases and product PQ increases. The range of unstable region shifts towards the small wave number k, as temperature ratio (T i /T e ) increases. The positron concentration and temperature ratio of positron to electron, change the unstable region slightly. As positron concentration increases both k min and k max for modulational instability increases and maximum value of the product PQ shifts towards the larger value of k. 相似文献
19.
B. R. Frieden 《Astrophysics and Space Science》1996,244(1-2):387-391
Fisher informationI is a classical concept that originates in estimation theory. Through the Cramer-Rao inequality, it defines the smallest possible error in the estimation of a parameter in the presence of noise obeying a given probability law. More recently, Fisher information has been incorporated within a variational principle for forming the laws of physics (Schrödinger wave equation, Dirac equation, etc.). The premise is thatdI/dt0, witht the time, so that, at equilibrium,I=min. The premise has recently been proven for any process obeying a Fokker-Planck differential equation. Hence, Fisher information provides a new measure of the passage of time. All errors of estimation increase, on average, with time. 相似文献
20.
S. Barcza 《Astrophysics and Space Science》1984,100(1-2):185-218
Eigenvalues and normalized wave functions of an electron are derived in the field of a generalized dipole with chargesZ
1 andZ
2 (Z
1+Z
2 0) in the asymptotic region up to the third order (inr
2) where the distance,r
2, between the two charges is small. These asymptotic wave functions render it possible to calculate the asymptotic expansion for the coefficients of a coupled infinite system of second order differential equations arising from a perturbative (analytic) solution to the Schrödinger equation of helium-like ions if the nuclear charge is not less than 2. 相似文献