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There are two conservation quantities needed to derive conservation laws of sine-Gordon equation in a frame of laboratory reference.one of them could be derived easily with a standard process,but the other could not .After the gauge transformation e^-iθσ2/2is introduced,we simply obtain the other one without any questionable assumption. 相似文献
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Since the Jost solutions of the derivative nonlinear Schrodinger equation do not tend to the free Jost solutions, when the spectral parameter tends to infinity(|A|→∞), the usual inverse scattering transform (IST) must be revised. If we take the parameter κ = λ^-1 as the basic parameter, the Jost solutions in the limit of |κ|→∞ do tend to the free Jost solutions, hence the usual procedure to construct the equations of IST in κ-plane remains effective. After we derive the equation of IST in terms of κ, we can obtain the equation of IST in λ-plane by the simple change of parameters λ = κ^-1. The procedure to derive the equation of IST is reasonable, and attention is never paid to the function W(x) introduced by the revisions of Kaup and Newell. Therefore, the revision of Kaup and Newell can be avoided. 相似文献
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系统地讨论了含修正项的KdV方程的直接微扰方法.从反散射变换所得的不含修正项方程的严格多孤子解出发,导出了线性化算子的零本征值的所有本征函数——平方Jost函数.引入了它们所对应的伴随函数和定义了内积.计算了应有的正交关系,并自然得到单位元的平方Jost函数的展开式.利用广义的Marchenko方程,证明了平方Jost函数的完备性.同时得到展开式中的积分是沿实轴从-∞到∞,但在原点附近将从上方绕过.这不同于过去所得的Cauchy主值积分.为最明确显示这一差别,在单孤子情况下又用平方Jost函数的显式,直接作了验证.同时指出,以前由于取Cauchy主值积分导出的KdV方程所特有的孤子尾,在采用从上方绕过原点的积分时,则事实上并不存在.
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A SOLITON PERTURBATION THEORY FOR THE UNSTABLE NONLINEAR SCHR?DINGER EQUATION WITH CORRECTIONS 下载免费PDF全文
Based on the Zakharov-Shabat equation of the inverse scattering transform for the unstable nonlinear Schr?dinger equation, for which a perturbation theory with corrections is developed in this paper. All necessary formulae for calculating the scattering data are derived. Based upon these formulae, the effect due to the corrections can be studied. As an example, the correction due to the damping is calculated. 相似文献
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An exact direct perturbation theory of nonlinear Schrodinger equation with corrections is developed under the condition that the initial value of the perturbed solution is equal to the value of an exact multisoliton solution at a particular time. After showing the squared Jost functions are the eigenfunctions of the linearized operator with a vanishing eigenvalue,suitable definitions of adjoint functions and inner product are introduced. Orthogonal relations are derived and the expansion of the unity in terms of the squared Jost functions is naturally implied. The completeness of the squared Jost functions is shown by the generalized Marchenko equation. As an example,the evolution of a Raman loss compensated soliton in an optical fiber is treated. 相似文献
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自从南氏发现π介子与核子散射中的著名的南氏不定性后,不少作者研究了各种弹性过程的分波分析中的运动学不定性,并给出了相应的物理解释。对非弹性过程迄今还没有进行仔细的研究。作为第一步,并为了实际上的目的,本文讨论π介子光致产生过程的分波分析中的不定性。 跃迁振幅可以写成如下形式: 相似文献
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