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1.
毕金钵 《上海大学学报(英文版)》2004,8(3):286-288
AA modified version of the bilinear Baecklund transformation for the MKdV equation was given, with which some new solutions of the MKdV equation are obtained. The approach used here is general and can be applied to other soliton equations. 相似文献
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孙业朋 《上海大学学报(英文版)》2005,9(6):471-475
1IntroductionIn recent years , the nonlinear integrable latticeequations have been extensively studied ,such as theAblowitz-Ladik lattice[1], the Toda lattice[2], thedifferential-difference KdVequation[3]and so on[4-7].Inthe theory of nonlinear integrable lattice equations ,ani mportant subject is to search for new Lax integrablelattice equations .In addition,several methods for de-termining exact solutions of soliton equations havebeen developed . The Darboux transformation ( DT)method pl… 相似文献
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The mixed AKNS nonlinear evolution equation in equation, which contains an isospectral term the AKNS system. So searching for its exact and a nonisospectral term, is an important solutions is vital both for the AKNS system and in mathematical sense. In this paper, the corresponding Lax pair was given, the bilinear forms of the mixed AKNS equation were obtained through introducing the transformation of dependent variables. By using Hirota＇s bilinear method, the N-soliton solutions were obtained. 相似文献
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The mixed AKNS equation, which contains an isospectral term and a nonisospectral term, is an important nonlinear evolution equation in the AKNS system. So searching for its exact solutions is vital both for the AKNS system and in mathematical sense. In this paper, the corresponding Lax pair was given, the bilinear forms of the mixed AKNS equation were obtained through introducing the transformation of dependent variables. By using Hirota's bilinear method, the N-soliton solutions were obtained. 相似文献
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The novel Wronskian solutions of the KdV equation were obtained as limits of the soliton solutions in the Wronskian form. These solutions were verified by direct substitution to satisfy the bilinear derivative form of the KdV equadon and its Backlund transformation. 相似文献
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A modified Lindstedt-Poincaré(LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equations are converted into a group of linear ordinary differential equations by introducing a set of simple transformations.An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modified method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation,and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales. 相似文献
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We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper. 相似文献
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微分差分KdV方程新的类多孤子解 总被引：3，自引：0，他引：3
This article is concerned with the Hirota direct method for studying novel multisoliton solutions of the discrete KdV equation.First the Hirota method was introduced,then the novel multisoliton solutions were obtained.Simultaneously the figures of the novel one-soliton solution and two-solton solution were given and the singularity of the novel multisoliton solutions was discussed.Finally it was pointed out that the multisoliton solutions with sigularity can be called soliton-like solutions. 相似文献
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In this paper,the relationship between the time-dependent solutions andsteady-state solutions of the semiconductor equations affected by magnetic field isconsidered.A decay estimate between the time-dependent solutions and steady-statesolutions is proved by a series of estimetes on the solutions under some conditions. 相似文献
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Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in nonlinear science. In this paper, the modified Boussinesq equation is derived from the modified Gel’fand-Dikii (mG-D) system.Furthermore, we study the modified Boussinesq equation by using the bilinear method and Wronskian technique, we obtain the N-soliton solutions to the above equation. 相似文献
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毕金钵 《上海大学学报(英文版)》2004,8(3)
A modified version of the bilinear Backlund transformation for the MKdV equation was given, with which some new solutions of the MKdV equation are obtained. The approach used here is general and can be applied to other soliton equations. 相似文献
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使用齐次平衡方法，得到了（2＋1）维破裂孤子方程的一些新多孤子解，齐次平衡方法，能使复杂的（2＋1）维破裂孤子方程转化为简单的线性偏微分方程和双线性偏微分方程，然后通过特定的拟解，便可构造出（2＋1）维破裂孤子方程的丰富的孤子结构。 相似文献
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Sine-Gordon(S-G)方程是可以应用于晶格错位系统的方程。通过引入双线性算子,经过等价变换得到用双线性导数表示的S-G方程。将用幂级数表示的函数代入变换后的方程求得方程的单孤子、双孤子的解析解,并用三维图象成功的展示了孤子随时间变化的相互作用过程。结果丰富了方程的非线性解并有助于其数学模型的理解和物理中的应用。 相似文献
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该文根据齐次平衡原则利用Hirota提出的非线性方程的双线性形和试探函数法推出二维kdv方程的二重孤立波解,这些孤立波解有助于人们认识波的传播性质。其解对于解释一些物理现象有一定的意义。 相似文献
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利用标准Painleve截断分析法,将Konopelehenko-Dubrovsky(KD)方程约化为两个线性偏微分方程和一个双线性偏微分方程,建立起相应的Backlund变换,进而获得该(2+1)维非线性系统的多孤子解. 相似文献
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By bilinear approach we derive N-soliton-like solutions for a variable coefficient KdV equation with some x-dependent coefficients. This equation can be considered as a non-isospectral variable coefficient KdV equation. Solutions in Hirota’s form and Wronskian form are given, respectively. 相似文献
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高校双语教学现状分析及建议 总被引：2，自引：0，他引：2
章雅荻 《重庆第二师范学院学报》2012,25(2):15-18
通过对重庆高校双语教学现状的分析,双语教学的重要性凸显出来,主要体现在三个方面：为国家培养21世纪新型复合型人才;为学生今后出国继续深造做好准备,使其更具国际竞争力;让教、学双方及时了解学科领域最前沿的理论和最新的学术成果。在此基础上,提出了四点建议。 相似文献