共查询到20条相似文献,搜索用时 62 毫秒
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本文利用行波约化方法,研究了用于描述飞秒光脉冲传输的高阶非线性薛定谔方程,得到了它的包络型Jacobian椭圆函数双周期解和孤波解.分析结果表明亮孤子的存在依赖于负三阶色散效应,暗孤子的存在依赖于正三阶色散效应. 相似文献
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高阶非线性薛定谔方程新一类孤波解的传输稳定性分析 总被引:1,自引:1,他引:0
本文针对最近发现的高阶NLSE的新一类孤波解,通过计算机模拟,对其在传输中的稳定性进行了分析。数值计算表明该孤波解的稳定性与入射脉冲幅度的取值有关,且对不同微扰其传输的稳定趋势及稳定程度不同。这对该孤波在实际中传输有一定指导意义。 相似文献
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研究了电磁感应透明介质中高阶非线性效应对光孤子传输的影响。采用半经典理论获得介质对光场的线性和非线性响应,基于介质特性利用波动理论推演出三-五阶非线性薛定谔方程。介质的线性非线性特性分别决定了群速度色散参量,三阶和五阶非线性系数。研究结果表明,该非线性介质既可以诱导亮孤子也可以诱导暗孤子,取决于群速度色散参量和三阶非线性系数。当前者为负同时后者为正时产生亮孤子,当两者均为负时产生暗孤子,二者可以通过载频与相应跃迁能级失谐的调节获得。与普通非线性薛定谔方程相比,三-五阶非线性薛定谔方程对亮孤子和暗孤子出现的参数和输入条件更加严格。 相似文献
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Some new exact travelling wave and period solutions of
discrete nonlinear Schrödinger equation are found
by using a hyperbolic tangent function approach, which was usually
presented to find exact travelling wave solutions of certain
nonlinear partial differential models. Now we can further extend
the new algorithm to other nonlinear differential-different models. 相似文献
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With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Schrödinger equation (GDNLSE) have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given. 相似文献
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A systematic method which is based on the classical Lie group reduction is used to find the novel exact solution of the cubic-quintic nonlinear Schrödinger equation (CQNLS) with varying dispersion, nonlinearity, and gain or absorption. Algebraic solitary-wave as well as kink-type solutions in three kinds of optical fibers represented by coefficient varying CQNLS equations are studied in detail. Some new exact solutions of optical solitary wave with a simple analytic form in these models are presented. Appropriate solitary wave solutions are applied to discuss soliton propagation in optical fibres, and the amplification and compression of pulses in optical fibre amplifiers. 相似文献
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WANG Ming-Liang ZHANG Jin-Liang LI Xiang-Zheng 《理论物理通讯》2008,50(7):39-42
With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation (GDNLSE) have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given. 相似文献
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By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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HUANGDing-Jiang ZHANGHong-Qing 《理论物理通讯》2004,42(2):171-174
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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By making use of the generalized sine-Gordon equation expansion method, we find cnoidal periodic wave solutions and fundamental bright and dark optical solitarywave solutions for the fourth-order dispersive and the quintic nonlinear Schrodinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves. 相似文献
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基于描述超短脉冲在超常介质中传输的非线性薛定谔方程,本文数值研究了高阶效应影响下高阶亮、暗孤子在超常介质中的传输情况。数值模拟表明,三阶色散和自陡峭效应都会引起高阶孤子的分裂和辐射,破坏高阶亮孤子周期性演化特性,导致高阶暗孤子分裂出的灰孤子不对称;孤子的阶数越高,三阶色散和自陡峭的影响越大。利用超常介质可控的色散和非线性特性,通过调节三阶色散和自陡峭效应的系数,发现超常介质中可以基本支持二阶亮孤子、二阶暗孤子和三阶暗孤子的稳定演化。本文的研究结果为将来进一步研究超常介质中高阶亮、暗孤子的存在及传输特性提供了一定的参考价值。 相似文献
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HAN Zhao-Xiu 《理论物理通讯》2007,47(1):10-14
The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication. 相似文献
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New Exact Travelling Wave Solutions to Kundu Equation 总被引:1,自引:0,他引:1
Based on a first-order nonlinear ordinary differential equation with Six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics. 相似文献