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1.
By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrfdinger type equations. It is shown that many exact periodic solutions of some nonlinear Schro^edinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions. 相似文献
2.
A class of nonlinear Schrödinger-type equations, including the Rangwala-Rao equation, the Gerdjikov-Ivanov equation, the Chen-Lee-Lin equation and the Ablowitz-Ramani-Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short). 相似文献
3.
Using the wave packet theory,we obtain all the solutions of the weakly damped nonlinear Schrodinger equation.These solutions are the static solution,and solutions of planar wave,solitary wave,shock wave and elliptic function wave and chaos.The bifurcation phenomenon exists in both steady and non-steady solutions.The chaotic and periodic motions can coexist in a certain parametric space region. 相似文献
4.
Solving coupled nonlinear Schrodinger equations via a direct discontinuous Galerkin method 下载免费PDF全文
In this work,we present the direct discontinuous Galerkin(DDG) method for the one-dimensional coupled nonlinear Schrdinger(CNLS) equation.We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system.The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method.Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations. 相似文献
5.
Conservation laws of the generalized nonlocal nonlinear Schrodinger equation 总被引:1,自引:0,他引:1 下载免费PDF全文
The derivations of several conservation laws of the generalized
nonlocal nonlinear Schr?dinger equation are presented. These
invariants are the number of particles, the momentum, the angular
momentum and the Hamiltonian in the quantum mechanical analogy. The
Lagrangian is also presented. 相似文献
6.
The coupled nonlinear Schodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions. 相似文献
7.
Instead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called He's variational iteration method (VIM) is introduced to be applied to solve nonlinear heat transfer equations in this Letter. In this research, variational iteration method is used to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative-conduction equation containing two small parameters of ε1 and ε2 and evaluate the efficiency of straight fins. VIM can apply to the nonlinear equations with boundary or initial conditions defined in different points just with developing the correction functional using the extra parameters such as Cn, as used in this Letter. 相似文献
8.
Jared C. Bronski David W. McLaughlin Michael J. Shelley 《Journal of statistical physics》1996,88(5-6):1077-1115
We study the problem of localization in a disordered one-dimensional nonlinear medium modeled by the nonlinear Schrödinger equation. Devillard and Souillard have shown that almost every time-harmonic solution of this random PDE exhibits localization. We consider the temporal stability of such time-harmonic solutions and derive bounds on the location of any unstable eigenvalues. By direct numerical determination of the eigenvalues we show that these time-harmonic solutions are typically unstable, and find the distribution of eigenvalues in the complex plane. The distributions are distinctly different for focusing and defocusing nonlinearities. We argue further that these instabilities are connected with resonances in a Schrödinger problem, and interpret the earlier numerical simulations of Caputo, Newell, and Shelley, and of Shelley in terms of these instabilities. Finally, in the defocusing case we are able to construct a family of asymptotic solutions which includes the stable limiting time-harmonic state observed in the simulations of Shelley. 相似文献
9.
为提高传统光滑粒子动力学(SPH)方法求解高维非线性薛定谔(nonlinear Schr?dinger/Gross-Pitaevskii equation, NLS/GP)方程的数值精度和计算效率,本文首先基于高阶时间分裂思想将非线性薛定谔方程分解成线性导数项和非线性项,其次拓展一阶对称SPH方法对复数域上线性导数部分进行显式求解,最后引入MPI并行技术,结合边界施加虚粒子方法给出一种能够准确、高效地求解高维NLS/GP方程的高阶分裂修正并行SPH方法.数值模拟中,首先对带有周期性和Dirichlet边界条件的NLS方程进行求解,并与解析解做对比,准确地得到了周期边界下孤立波的奇异性,且对提出方法的数值精度、收敛速度和计算效率进行了分析;随后,运用给出的高阶分裂粒子方法对复杂二维和三维NLS/GP问题进行了数值预测,并与其他数值结果进行比较,准确地展现了非线性孤立波传播中的奇异现象和玻色-爱因斯坦凝聚态中带外旋转项的量子涡旋变化过程. 相似文献
10.
本文为了获得非线性发展方程新的无穷序列精确解,给出了几种辅助方程的Böcklund变换和解的非线性叠加公式,并构造了一些非线性发展方程新的无穷序列精确解,其中包括无穷序列Jacobi椭圆函数解、无穷序列双曲函数解和无穷序列三角函数解.该方法在构造非线性发展方程无穷序列精确解方面具有普遍意义.
关键词:
辅助方程法
解的非线性叠加公式
无穷序列解
非线性发展方程 相似文献
11.
Christopher Chong Dmitry E. Pelinovsky Guido Schneider 《Physica D: Nonlinear Phenomena》2012,241(2):115-124
The variational approximation is a well known tool to approximate localized states in nonlinear systems. In the context of a discrete nonlinear Schrödinger equation with a small coupling constant, we prove error estimates for the variational approximations of site-symmetric, bond-symmetric, and twisted discrete solitons. This is shown for various trial configurations, which become increasingly more accurate as more parameters are taken. It is also shown that the variational approximation yields the correct spectral stability result and controls the oscillatory dynamics of stable discrete solitons for long but finite time intervals. 相似文献
12.
YUAN Qing-Xin DING Guo-Hui 《理论物理通讯》2006,46(5):873-878
For Bose-Einstein condensates trapped in a harmonic potential well, we present numerical results from solving the tlme-dependent nonlinear Schrolinger equation based on the Crank-Nicolson method. With this method we are able to find the ground state wave function and energy by evolving the trial initial wave function in real and imaginary time spaces, respectively. In real time space, the results are in agreement with [Phys. Rev. A 51 (1995) 4704], but the trial wave function is restricted in a very small range. On the contrary, in imaginary time space, the trial wave function can be chosen widely, moreover, the results are stable. 相似文献
13.
Miki Wadati 《Pramana》2001,57(5-6):841-847
As an introduction to the special issue on nonlinear waves, solitons and their significance in physics are reviewed. The soliton
is the first universal concept in nonlinear science. Universality and ubiquity of the soliton concept are emphasized. 相似文献
14.
15.
By means of symbolic computation, a new application of Riccati equation is presented to obtain novel exact solutions of some nonlinear evolution equations, such as nonlinear Klein-Gordon equation, generalized Pochhammer-Chree equation and nonlinear Schrödinger equation. Comparing with the existing tanh methods and the proposed modifications, we obtain the exact solutions in the form as a non-integer power polynomial of tanh (or tan) functions by using this method, and the availability of symbolic computation is demonstrated. 相似文献
16.
Following Salpeter, the Bethe-Salpeter equation for the bound system of two oppositely charged particles is reduced to a Schrödinger equation for each of the following cases: (a) both particles are spin 1/2 particles, (b) one particle is a spinor while the other is spinless, and (c) both particles are spinless. It is shown that ife is the magnitude of charge carried by each of the particles whose masses are set equal to the electron and proton masses then, strictly speaking, only in case (a) do we obtain the familiar Schrödinger equation for the hydrogen atom. The latter equation is recovered in the other two cases only if relativistic remnants—terms of the order of 10?5 and smaller—are neglected in comparison with unity. Attention is drawn to a situation where such remnants may not be negligibly small, viz. the problem of confinement of quarks. 相似文献
17.
In this paper, we study the existence conditions of the soliton solutions induced by considering the higher-order effects
such as the third-order dispersion (TOD), self-steepening (SS), and self-frequency shift arising from stimulated Raman scattering
(SRS) simultaneously in optical soliton communication. Based on the Jacobian expansion method, we successfully obtain bright
and dark solitons. The results shows that the resultant inclusion is in agreement with Mollenauer et al. [Physical Review Letters 45 (1980) 1095] when the SRS is not considered; while when the SRS is considered, the existence conditions of the higher-order
effects induced bright and dark solitons are not only quite different from those of the group velocity dispersion (GVD)-induced
and self-phase modulation (SPM)-induced solitons, but also different from those of the TOD- and SS-induced solitons discussed
by Mollenauer et al. [Physical Review Letters 45 (1980) 1095]. 相似文献
18.
The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions. 相似文献
19.
Variational iteration method is implemented to construct solitary solutions for nonlinear dispersive equations. In this scheme the solution takes the form of a convergent series with easily computable components. The chosen initial solution or trial function plays a major role in changing the physical structure of the solution. Many models are approached and the obtained results reveal that the method is very effective and convenient for constructing solitary solutions. 相似文献