共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we investigate nonlinear the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y. Zhang, et al., Appl. Math. Comput. 216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM), Cosine-function method (CFM). We show that the solutions by using ISM and CFM are equal. Finally, we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM). 相似文献
2.
Zhenya Yan 《Physics letters. A》2010,374(48):4838-4843
Analytical solutions are reported for the generalized non-integrable nonlinear Schrödinger equation with varying coefficients using the similarity transformation and tri-function method, which involve three free functions of spaces to generate abundant wave structures. Three types of free functions are chosen to exhibit the corresponding nonlinear wave propagations. 相似文献
3.
This paper obtains solitons and singular periodic solutions to the generalized resonant dispersive nonlinear Schrödinger’ equation with power law nonlinearity. There are several integration tools that are adopted to extract these solutions. They are simplest equation method, functional variable method, sine–cosine function method, tanh function method and the G′/G-expansion method. These integration techniques reveal bright and singular solitons as well as the corresponding singular periodic solutions to the nonlinear evolution equation. These solitons solutions are important in the nonlinear fiber optics community as well as in the study of rogue waves. 相似文献
4.
In this paper, by using the bifurcation method of dynamical systems, we derive the traveling wave solutions of the nonlinear equation UUτyy ? UyUτy + U2Uτ + 3Uy = 0. Based on the relationship of the solutions between the Novikov equation and the nonlinear equation, we present the parametric representations of the smooth and nonsmooth soliton solutions for the Novikov equation with cubic nonlinearity. These solutions contain peaked soliton, smooth soliton, W-shaped soliton and periodic solutions. Our work extends some previous results. 相似文献
5.
Based on the Hirota’s method, the multiple-pole solutions of the focusing Schrödinger equation are derived directly by introducing some new ingenious limit methods. We have carefully investigated these multi-pole solutions from three perspectives: rigorous mathematical expressions, vivid images, and asymptotic behavior. Moreover, there are two kinds of interactions between multiple-pole solutions: when two multiple-pole solutions have different velocities, they will collide for a short time; when two multiple-pole solutions have very close velocities, a long time coupling will occur. The last important point is that this method of obtaining multiple-pole solutions can also be used to derive the degeneration of N-breather solutions. The method mentioned in this paper can be extended to the derivative Schrödinger equation, Sine-Gorden equation, mKdV equation and so on. 相似文献
6.
Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order 下载免费PDF全文
In this paper, the travelling wave solutions for the generalized
Burgers--Huxley equation with nonlinear terms of any order are
studied. By using the first integral method, which is based on the
divisor theorem, some exact explicit travelling solitary wave
solutions for the above equation are obtained. As a result, some
minor errors and some known results in the previousl literature
are clarified and improved. 相似文献
7.
提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统. 相似文献
8.
9.
In this paper, the resonant nonlinear Schrödinger's equation is studied with three forms of nonlinearity. This equation is also considered with time-dependent coefficients. The first integral method is used to carry out the integration. Exact soliton solutions of this equation are found. These solutions are constructed through the established first integrals. The power of this manageable method is confirmed. 相似文献
10.
By means of the similarity transformation connecting with the solvable stationary equation, the self-similar combined Jacobian elliptic function solutions and fractional form solutions of the generalized nonlinear Schrödinger equation (NLSE) are obtained when the dispersion, nonlinearity, and gain or absorption are varied. The propagation dynamics in a periodic distributed amplification system is investigated. Self-similar cnoidal waves and corresponding localized waves including bright and dark similaritons (or solitons) for NLSE and arch and kink similaritons (or solitons) for cubic-quintic NLSE are analyzed. The results show that the intensity and the width of chirped cnoidal waves (or similaritons) change more distinctly than that of chirp-free counterparts (or solitons). 相似文献
11.
?smail Aslan 《Physics letters. A》2011,375(47):4214-4217
We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G′/G)-expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are constructed; hyperbolic, trigonometric, and rational which have not been explicitly computed before. 相似文献
12.
13.
Soliton,breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints 下载免费PDF全文
《中国物理 B》2021,30(6):60202-060202
The nonlinear Schro¨dinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schro¨dinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schro¨dinger equation can be well reconstructed by utilizing this physically-constrained deep learning method. 相似文献
14.
Muhammad Younis Tukur Abdulkadir Sulaiman Muhammad Bilal Shafqat Ur Rehman Usman Younas 《理论物理通讯》2020,72(6):65001
This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrödinger equation, which models the propagation of rogue waves in ocean engineering. The extended Fan sub-equation method with five parameters is used to find exact traveling wave solutions. It has been observed that the equation exhibits a collection of traveling wave solutions for limiting values of parameters. This method is beneficial for solving nonlinear partial differential equations, because it is not only useful for finding the new exact traveling wave solutions, but also gives us the solutions obtained previously by the usage of other techniques (Riccati equation, or first-kind elliptic equation, or the generalized Riccati equation as mapping equation, or auxiliary ordinary differential equation method) in a combined approach. Moreover, by means of the concept of linear stability, we prove that the governing model is stable. 3D figures are plotted for showing the physical behavior of the obtained solutions for the different values of unknown parameters with constraint conditions. 相似文献
15.
The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented. 相似文献
16.
In this paper, we construct the Darboux transformation (DT) for the reverse-time integrable nonlocal nonlinear Schrödinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions. Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula. 相似文献
17.
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schrödinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions. 相似文献
18.
In this paper, by virtue of symbolic computation, the investigation is made on a generalized variable-coefficient higher-order nonlinear Schrödinger equation with varying higher-order effects and gain or loss, which can describe the femtosecond optical pulse propagation in a monomode dielectric waveguide. A modified dependent variable transformation is introduced into the bilinear method to transform such an equation into a variable-coefficient bilinear form. Based on the formal parameter expansion technique, the multi-soliton solutions of this equation are obtained through the bilinear form under sets of parametric constraints. A Bäcklund transformation in bilinear form is also obtained for the first time in this paper. Finally, discussions on the analytic soliton solutions are given and various propagation situations are illustrated. 相似文献
19.
In this paper, by means of similarity transfomations, we obtain explicit solutions to the cubic--quintic nonlinear Schrödinger equation with varying coefficients, which involve four free functions of space. Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations. 相似文献