共查询到19条相似文献,搜索用时 296 毫秒
1.
Starting from the traveling wave solution, in small amplitude approximation, the Sine-Gordon equation can be re- duced to a generalized Duffing equation to describe the dislocation motion in a superlattice, and the phase plane properties of the system phase plane are described in the absence of an applied field. The stabilities are also discussed in the presence of an applied field. It is pointed out that the separatrix orbit describing the dislocation motion as the kink wave may transfer the energy along the dislocation line, keep its form unchanged, and reveal the soliton wave properties of the dislocation motion. It is stressed that the dislocation motion process is the energy transfer and release process, and the system is stable when its energy is minimum. 相似文献
2.
Studying with the asymptotic iteration method, we present approximate solutions of the Dirac equation for the Eckart potential in the case of position-dependent mass. The centrifugal term is approximated by an exponential form, and the relativistic energy spectrum and the normalized eigenfunctions are obtained explicitly. 相似文献
3.
The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the unitary coupled-channel approximation. In addition to the Weinberg-Tomozawa term, the contribution of the s-and u-channel potentials in the-wave approximation are taken into account. In the sector of isospin I=1/2 and strangeness S =0, a pole is detected in a reasonable region of the complex energy plane of ■ in the center-of-mass frame by analyzing the behavior of the scattering amplitude, which is higher than the ηN threshold and lies on the third Riemann sheet. Thus, it can be regarded as a resonance state and might correspond to the N(1535) particle of the Particle Data Group(PDG) review. The coupling constants of this resonance state to the πN,ηN,KΛ and KΣ channels are calculated, and it is found that this resonance state couples strongly to the hidden strange channels. Apparently, the hidden strange channels play an important role in the generation of resonance states with strangeness zero. The interaction of the pseudoscalar meson and the baryon octet is repulsive in the sector of isospin I = 3/2 and strangeness S = 0, so that no resonance state can be generated dynamically. 相似文献
4.
The spin-weighted spheroidal equation in the case of s = 1 is studied. By transforming the independent variables, we make it take the Schrdinger-like form. This Schrdinger-like equation is very interesting in itself. We investigate it by using super-symmetric quantum mechanics and obtain the ground eigenvalue and eigenfunction, which are consistent with the results previously obtained. 相似文献
5.
By truncating the Painleve expansion at the constant level term, the Hirota bilinear form is obtained for a (3+1)-dimensional variable-coefficient Kadomtsev Petviashvili equation. Based on its bilinear form, solitary-wave solutions are constructed via the ε-expansion method and the corresponding graphical analysis is given. Furthermore, the exact solution in the Wronskian form is presented and proved by direct substitution into the bilinear equation. 相似文献
6.
《中国物理 B》2020,(2)
Nonlinear evolution of multiple toroidal Alfven eigenmodes(TAEs) driven by fast ions is self-consistently investigated by kinetic simulations in toroidal plasmas.To clearly identify the effect of nonlinear coupling on the beam ion loss,simulations over single-n modes are also carried out and compared with those over multiple-n modes,and the wave-particle resonance and particle trajectory of lost ions in phase space are analyzed in detail.It is found that in the multiple-n case,the resonance overlap occurs so that the fast ion loss level is rather higher than the sum loss level that represents the summation of loss over all single-n modes in the single-n case.Moreover,increasing fast ion beta β_h can not only significantly increase the loss level in the multiple-n case but also significantly increase the loss level increment between the single-n and multiple-n cases.For example,the loss level in the multiple-n case for β_h=6.0% can even reach 13% of the beam ions and is 44% higher than the sum loss level calculated from all individual single-n modes in the single-n case.On the other hand,when the closely spaced resonance overlap occurs in the multiple-n case,the release of mode energy is increased so that the widely spaced resonances can also take place.In addition,phase space characterization is obtained in both single-n and multiple-n cases. 相似文献
7.
In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model. 相似文献
8.
《中国物理 B》2019,(1)
A semi-empirical equation of state model for aluminum in a warm dense matter regime is constructed. The equation of state, which is subdivided into a cold term, thermal contributions of ions and electrons, covers a broad range of phase diagram from solid state to plasma state. The cold term and thermal contribution of ions are from the Bushman–Lomonosov model, in which several undetermined parameters are fitted based on equation of state theories and specific experimental data. The Thomas–Fermi–Kirzhnits model is employed to estimate the thermal contribution of electrons. Some practical modifications are introduced to the Thomas–Fermi–Kirzhnits model to improve the prediction of the equation of state model. Theoretical calculation of thermodynamic parameters, including phase diagram, curves of isothermal compression at ambient temperature, melting, and Hugoniot, are analyzed and compared with relevant experimental data and other theoretical evaluations. 相似文献
9.
The spin-weighted spheroidal equation in the case of s=1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics.The first-five terms of the superpotential in the series of parameter β are given.The general form for the n-th term of the superpotential is also obtained,which could also be derived from the previous terms W k,k < n.From these results,it is easy to obtain the ground eigenfunction of the equation.Furthermore,the shape-invariance property in the series of parameter β is investigated and is proven to be kept.This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics.We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β. 相似文献
10.
The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained. 相似文献
11.
A. H. Khater M. M. Hassan E. V. Krishnan Y. Z. Peng 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(2):177-184
New several classes of exact solutions are obtained in terms of the
Weierstrass elliptic function for some nonlinear partial
differential equations modeling ion-acoustic waves as well as dusty
plasmas in laboratory and space sciences. The Weierstrass elliptic
function solutions of the Schamel equation, a fifth order dispersive
wave equation and the Kawahara equation are constructed. Moreover,
Jacobi elliptic function solutions and solitary wave solutions of
the Schamel equation are also given. The stability of some periodic
wave solutions is computationally
studied. 相似文献
12.
YAN Zhen-Ya 《理论物理通讯》2005,43(3):391-396
Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem
solving soliton equations into
another one solving the corresponding set of nonlinear algebraic equations.
With the aid of Maple, we choose the modified KdV equation,
(2+1)-dimensional KP equation,
and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm.
As a consequence, many types of new doubly periodic solutions are obtained
in terms of the Weierstrass elliptic function. Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple
limits of doubly periodic solutions. 相似文献
13.
《Journal of Geometry and Physics》2001,39(1):51-62
Closed loop solitons in a plane, whose curvatures obey the modified Korteweg–de Vries equation, were investigated. It was shown that their tangential vectors are expressed by ratio of Weierstrass sigma functions for genus one case and ratio of Baker’s sigma functions for the genus two case. This study is closely related to classical and quantized elastica problems. 相似文献
14.
15.
We study the dynamics of the cubic–quintic nonlinear Schr?dinger equation by the symplectic method. The behaviors of the equation are discussed with harmonically modulated initial conditions, and the contributions from the quintic term are discussed. We observe the elliptic orbit, homoclinic orbit crossing, quasirecurrence, and stochastic motion with different nonlinear parameters in this system. Numerical simulations show that the changing processes of the motion of the system and the trajectories in the phase space are various for different cubic nonlinear parameters with the increase of the quintic nonlinear parameter. 相似文献
16.
YANZhen-Ya 《理论物理通讯》2004,42(5):645-648
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions. 相似文献
17.
18.
In this paper, a new special ansatz solution, where elliptic
equation satisfied by elliptic functions is taken as an
intermediate transformation, is applied to solve the
KdV-Burgers-Kuramoto equation, and many more new periodic
solutions are obtained, including solutions expressed in terms of
Jacobi elliptic functions, solution expressed in terms of
Weierstrass elliptic function. 相似文献
19.
The study of polynomial solutions to the classical Lamé equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schrödinger equation with finite gap potential given by the Weierstrass $\wpThe study of polynomial solutions to the classical Lamé equation in its algebraic form, or equivalently, of double-periodic
solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and
their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr?dinger equation
with finite gap potential given by the Weierstrass -function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric
and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when
the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation
with four singularities. 相似文献