共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper,we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear Schrdinger equation (NLS) with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions,one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results,some previous one-and two-soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one-and the two-soliton and the discussion about the integrability property and the Hirota method is given finally. 相似文献
2.
We investigate the one-dimensional nonlinear SchrSdinger equation with a perturbation of polynomial type. The approximate symmetries and approximate symmetry reduction equations are obtained with the approximate symmetry perturbation theory. 相似文献
3.
Approximate analytic solutions for a generalized Hirota—Satsuma coupled KdV equation and a coupled mKdV equation
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
<正>This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries(KdV) equation and a coupled modified Korteweg-de Vries(mKdV) equation. This method provides a sequence of functions which converges to the exact solution of the problem and is based on the use of the Lagrange multiplier for the identification of optimal values of parameters in a functional.Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions. 相似文献
4.
We introduce an approach that combines a similarity method with several transformations to find analytical solitary wave solutions for a generalized space- and time-variable coefficients of nonlinear Schrödinger equation with higher-order terms with consideration of varying dispersion, higher nonlinearities, gain/loss and external potential. One of these transformations is constructed in such a way that allows study of the width of localized solutions. Solitary-like wave solutions for front, bright and dark are given. The precise expressions of the soliton?s width, peak, and the trajectory of its mass center and the external potential which are symbol of dynamic behavior of these solutions, are investigated analytically. In addition, the dynamical behavior of moving, periodic, quasi-periodic of breathing, and resonant are discussed. Stability of the obtained solutions is analyzed both analytically and numerically. 相似文献
5.
6.
7.
This paper presents a meshless method for the nonlinear generalized regularized long wave(GRLW) equation based on the moving least-squares approximation.The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method.A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm.Compared with numerical methods based on mesh,the meshless method for the GRLW equation only requires the scattered nodes instead of meshing the domain of the problem.Some examples,such as the propagation of single soliton and the interaction of two solitary waves,are given to show the effectiveness of the meshless method. 相似文献
8.
Under investigation in this paper is a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics. Soliton and one-periodic-wave solutions are obtained via the Hirota bilinear method and Hirota–Riemann method. Magnitude and velocity of the one soliton are derived. Graphs are presented to discuss the solitons and one-periodic waves: the coefficients in the equation can determine the velocity components of the one soliton, but cannot alter the soliton magnitude; the interaction between the two solitons is elastic; the coefficients in the equation can influence the periods and velocities of the periodic waves. Relation between the one-soliton solution and one-periodic wave solution is investigated. 相似文献
9.
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
10.
Bilinear Backlund transformation and explicit solutions for a nonlinear evolution equation
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
The bilinear form of two nonlinear evolution equations are derived by using Hirota derivative. The Backlund transformation based on the Hirota bilinear method for these two equations are presented, respectively. As an application, the explicit solutions including soliton and stationary rational solutions for these two equations are obtained. 相似文献
11.
Trial function method and exact solutions to the generalized nonlinear Schrodinger equation with time-dependent coefficient
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions. 相似文献
12.
Robert Conte K.W. Chow 《理论物理通讯》2006,46(6):961-965
The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system. 相似文献
13.
New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation 总被引:2,自引:0,他引:2
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper,
based on hyperbolic tanh-function method and homogeneous balance
method, and auxiliary equation method, some new exact solitary
solutions to the generalized mKdV equation and generalized
Zakharov--Kuzentsov equation are constructed by the method of
auxiliary equation with function transformation with aid of
symbolic computation system Mathematica. The method is of important
significance in seeking new exact solutions to the evolution
equation with arbitrary nonlinear term. 相似文献
14.
G. Adomian 《Foundations of Physics Letters》1995,8(1):99-101
Nonlinear nonlocal equations of mathematical physics such as the K.P.P. equation, the generalized nonlinear Schrödinger equation, the Witham equation for water waves et al. are solved by decomposition. 相似文献
15.
16.
The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
This paper studies a generalized nonlinear evolution equation. Using
the homotopic mapping method, it constructs a corresponding homotopic
mapping transform. Selecting a suitable initial approximation and
using homotopic mapping, it obtains an approximate solution with an
arbitrary degree of accuracy for the solitary wave. From the
approximate solution obtained by using the homotopic mapping method, it
possesses a good accuracy. 相似文献
17.
Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
This paper is concerned with the generalized variable-coefficient nonlinear evolution equation(vc-NLEE).The complete integrability classification is presented,and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlev′e analysis.Then,the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method,and the Lax pairs(LP) of the vc-NLEEs are constructed in terms of the integrable conditions. 相似文献
18.
Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
19.
E. Tala-Tebue Z.I. Djoufack A. Djimeli-Tsajio A. Kenfack-Jiotsa 《Chinese Journal of Physics (Taipei)》2018,56(3):1232-1246
In order to investigate the nonlinear fractional Zoomeron equation, we propose three methods, namely the Jacobi elliptic function rational expansion method, the exponential rational function method and the new Jacobi elliptic function expansion method. Many kinds of solutions are obtained and the existence of these solutions is determined. For some parameters, these solutions can degenerate to the envelope shock wave solutions and the envelope solitary wave solutions. A comparison of our new results with the well-known results is made. The methods used here can also be applicable to other nonlinear partial differential equations. The fractional derivatives in this work are described in the modified Riemann–Liouville sense. 相似文献
20.
《Physics letters. A》2020,384(13):126264
We explore novel excitations in the form of nonlinear local waves, which are described by the sinh-Gordon (SHG) equation with a variable coefficient. With the aid of the self-similarity transformation, we establish the relationship between solutions of the SHG equation with a variable coefficient and those of the standard SHG equation. Then, using the Hirota bilinear method, we obtain a more general bilinear form for the standard SHG equation and find new one- and two-soliton waves whose forms involve two arbitrary self-similarity functions. By an appropriate choice of the smooth self-similarity functions, we determine and display novel localized waves, and discuss their properties. The method used here can be extended to the three- and higher order soliton solutions. 相似文献