共查询到16条相似文献,搜索用时 250 毫秒
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利用扩展的双曲函数法得到了combined KdV-mKdV (cKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为cKdV方程的扭结状或钟状孤波解.理论分析表明,cKdV方程既有传播型孤立波解,也有非传播型孤立波解.文中对双扭结型孤立波解的稳定性进行了数值研究,结果表明,cKdV方程既存在稳定的双扭结型孤立波,也存在不稳定的双扭结型孤立波.
关键词:
cKdV方程
双扭结单孤子
稳定性 相似文献
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采用双曲函数展开法得到Modified Benjamin-Bona-Mahony(mBBM)方程的一类扭结-反扭结状的双扭结孤立波解,在不同的极限情况下,此孤立波分别退化为mBBM方程的扭结状和钟状孤立波解.对双扭结型单孤子的结构特征进行分析,构造有限差分格式对其动力学稳定性进行数值研究.有限差分格式为两层隐式格式,在线性化意义下无条件稳定.数值结果表明mBBM方程的双扭结型单孤子在不同类型的扰动下均具有很强的稳定性.对双孤立波的碰撞进行数值模拟,发现既存在弹性碰撞也存在非弹性碰撞. 相似文献
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通过线性稳定性分析,得到了多前车速度差模型的稳定性条件, 并发现通过调节多前车信息,使交通流的稳定区域明显扩大. 通过约化摄动方法 研究了该模型的非线性动力学特性:在稳定流区域,得到了描述密度波的Burgers方程;在交 通流的不稳定区域内,在临界点附近获得了描述车头间距的修正的Korteweg-de Vries (modified Korteweg-de Vries, mKdV)方程; 在亚稳态区域内,在中性稳定曲线附近获得了描述车头间距 的KdV方程. Burgers的孤波解、mKdV方程的扭结-反扭结波解及KdV方程的 孤波解描述了交通流堵塞现象. 相似文献
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The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. 相似文献
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It is shown that the heat-kernel expansion (rather than the gradient expansion) of the effective chiral action of the quark loop yields in next-to-leading (i.e., fourth) order an effective low-energy lagrangian which possesses stable soliton solutions. The baryon number-one soliton solution of this effective chiral lagrangian is found numerically. 相似文献
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In this paper, we present solutions for the nonlinear Schrödinger (NLS) equation with spatially inhomogeneous nonlinearities describing propagation of light in nonlinear media, under two sets of transverse modulation forms of inhomogeneous nonlinearity. The bright soliton solution and Gaussian solution have been obtained for one set of inhomogeneous nonlinearity modulation. For the other, bright soliton solution, black soliton solution and the train solution have been presented. Stability of the solutions has been determined by exact soliton solutions under certain conditions. 相似文献
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在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schrödinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schrödinger方程转化成非线性Schrödinger方程,并利用已知解深入研究变系数非线性Schrödinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论.
关键词:
非线性Schrö
dinger方程
相似变换
变系数
孤子解 相似文献
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Exact analytical solutions of three-dimensional Gross-Pitaevskii equation with time-space modulation 下载免费PDF全文
By the generalized sub-equation expansion method and symbolic computation,this paper investigates the(3 + 1)dimensional Gross-Pitaevskii equation with time-and space-dependent potential,time-dependent nonlinearity,and gain or loss.As a result,rich exact analytical solutions are obtained,which include bright and dark solitons,Jacobi elliptic function solutions and Weierstrass elliptic function solutions.With computer simulation,the main evolution features of some of these solutions are shown by some figures.Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management. 相似文献
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In this paper, by applying the extended Jacobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained. 相似文献