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引进五阶线性色散项方程K(m,n,1),用逆算符方法得到了sin型多重compacton 解(紧孤立波解);利用齐次平衡法得到了K(2,2,1)方程的Backlund变换,并且得到一些新的孤立波解;最后研究了sin型多重compacton解的线性稳定性. 相似文献
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通过数值求解由Miles导出的目前公认的的非传播孤立波的控制方程——一个带复共轭项的非线性立方SchrLdinger方程,对非传播孤立波进行研究。讨论了Miles方程中的线性阻尼系数α的值,计算表明,线性阻尼α对形成稳定的非传播孤立波影响很大,Laedke等人关于非传播孤立波的稳定性条件只是一个必要条件,而不是充分条件。模拟了两个非传播孤立波的相互作用,数值模拟表明,两个波的作用模式依赖于系统的参数,对不同的初始扰动及其演化的计算表明,只有适当的初始扰动才能形成单个稳定的非传播孤立波,否则扰动可能消失或发展成多个孤立波。 相似文献
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利用一个独立变换和动力系统方法对Fokas方程:u_(tx)=(1+v(?)■_x~2)sin(u),x∈R,t0进行研究.在对该方程所对应的平面动力系统进行定性分析的基础上,得到了该方程所有可能的显式孤立尖波解和周期尖波解. 相似文献
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本文考察George Green 1839年关于孤立波的论文的产生背景、研究方法及影响.Green自身的科学素养、剑桥的氛围以及罗素的报告促成了他的孤立波研究,其基本思想和处理方法被19世纪一些重要的孤立波研究者不同程度继承借鉴,对孤立波理论研究产生了重要影响. 相似文献
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本文运用摄动法和WKB方法(多尺度方法), 从位涡守恒方程出发,
分析旋转层结大气中基本流有垂直切变以及层结效应对$\beta$效应、地形效应和强迫耗散共同作用下的Rossby波的影响,
得到一个非标准形式的非线性Schr\"{o}dinger方程,而在水平波数小于3时该方程有包络孤立波解;
又进一步说明基本流的垂直切变对包络Rossby孤立波的波速的影响;强迫耗散对包络Rossby孤立波稳定度的影响.另外, 本
文还应用常数变异法求解了非齐次的Bessel方程, 得到包络Rossby孤立波的经向结构. 相似文献
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Anjan Biswas 《Applied Mathematics Letters》2009,22(2):208-210
The travelling wave ansatz is used to find the solitary wave solution of the generalized Kawahara equation. The ansatz is obtained from the structure of the soliton solution of the Kawahara equation and the modified Kawahara equation. The first two integrals of motion of the generalized Kawahara equation are also computed in this work. 相似文献
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Amin Esfahani 《Applied Mathematics Letters》2011,24(2):204-209
In this work, we study the perturbed nonlinear Klein–Gordon equation. We shall use the sech-ansätze method to derive the solitary wave solutions of this equation. 相似文献
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The one-dimensional Euler–Poisson system arises in the study of phenomena of plasma such as plasma solitons, plasma sheaths, and double layers. When the system is rescaled by the Gardner–Morikawa transformation, the rescaled system is known to be formally approximated by the Korteweg–de Vries (KdV) equation. In light of this, we show existence of solitary wave solutions of the Euler–Poisson system in the stretched moving frame given by the transformation, and prove that they converge to the solitary wave solution of the associated KdV equation as the small amplitude parameter tends to zero. Our results assert that the formal expansion for the rescaled system is mathematically valid in the presence of solitary waves and justify Sagdeev's formal approximation for the solitary wave solutions of the pressureless Euler–Poisson system. Our work extends to the isothermal case. 相似文献
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S.M. Hoseini 《Applied mathematics and computation》2010,216(12):3642-3651
Soliton perturbation theory is used to determine the evolution of a solitary wave described by a perturbed nonlinear Schrödinger equation. Perturbation terms, which model wide classes of physically relevant perturbations, are considered. An analytical solution is found for the first-order correction of the evolving solitary wave. This solution for the solitary wave tail is in integral form and an explicit expression is found, for large time. Singularity theory, usually used for combustion problems, is applied to the large time expression for the solitary wave tail. Analytical results are obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks, in the solitary wave tail. Two examples, the near-continuum limit of a discrete NLS equation and an explicit numerical scheme for the NLS equation, are considered in detail. For the discrete NLS equation it is found that three qualitatively different types of solitary wave tail can occur, while for the explicit finite-difference scheme, only one type of solitary wave tail occurs. An excellent comparison between the perturbation solution and numerical simulations, for the solitary wave tail, is found for both examples. 相似文献
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《Mathematical and Computer Modelling》2007,45(3-4):473-479
In this work, the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation is studied. The tanh–sech method, the cosh–sinh method and exponential functions method are efficiently employed to handle this equation. By means of these methods, the solitary wave, periodic wave and kink solutions are formally obtained. 相似文献
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In this work we devise an algebraic method to uniformly construct solitary wave solutions and doubly periodic wave solutions of physical interest for the Kersten–Krasil’shchik coupled KdV–mKdV system. This system as the classical part of one of superextension of the KdV equation was proposed very recently. The complete integrability, singular analysis and Lax pairs for this system have been found, but its exact solution are still unknown. 相似文献
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The hyperbolic function method for nonlinear wave equations is presented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Gr?bner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions. 相似文献
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This paper deals with a class of generalized KdV equation by making use of a mathematical technique based on using integral factors for solving differential equations and give rise to the solitary wave, periodic cusp wave and periodic wave solutions. The work confirms the power of the proposed method. 相似文献