Inverse scattering method and soliton double solution family for string effective action

A so-called modified Hauser-Ernst-type extended double-complex linear system is established and used to develop a new inverse scattering method for solving the equations of motion of the string effective action describing the coupled gravity, dilaton and Kalb-Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the application of the inverse scattering method fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.      

求解DNLS方程的反散射法的基本问题

对DNLS方程, 反散射法应选取k²=p为基本谱参数, 其中k为通常谱参数. 并引入一个新的谱参数及一个规范变换, 由此得到自由Jost解的规范正交系, 这就是反散射法的基本问题. 同时还得到了基于谱参数p的Marchenko方程和Zakharov-Shabat反散射方程. 关键词： DNLS方程 反散射法 自由Jost解 规范正交系     

Inverse scattering method and soliton solutionfamily for the Einstein--Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.     

Soliton solution to the complex modified Korteweg–de Vries equation on both zero and nonzero background via the robust inverse scattering method

In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background. Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time $t$ is large, then we give the comparison between the exact solution and the asymptotic solution.     

量子可积系统和量子反散射方法简介(续)

4 .3　ＸＸＸ模型的本征值问题 ,Ｂｅｔｈｅ假设方程ｔ(ｕ)的本征值问题实际上也是Ｔ(ｕ)的本征值问题 ,它涉及到Ｔ(ｕ)的对角化问题 ,也就是说 ,对辅助空间选什么样的基矢可使Ｔ(ｕ)的表示是对角的 .1 )ＴＮ(ｕ)的矩阵元之间的对易关系在关于谐振子问题的描述中 ,我们已看到算符之间的对易关系的作用 .现在我们需要的是Ｔ(ｕ)的矩阵元之间的对易关系 ,实际上它们已经包含在ＹＢ关系中了 .前面已经指出 ,Ｔ(ｕ)相对于辅助空间为矩阵 ,这涉及到Ｖ的基矢的问题 .在Ｖ中选取自然基 :|ｅ+ 〉 =10 ,|ｅ- 〉 =01 ( 4 0 )则Ｖ Ｖ =Ｃ2 Ｃ2 中的自…     

Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length

The evolution of solitons in Bose--Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature ({\em Phys. Rev. Lett.} {\bf 94} (2005) 050402 and {\em Chin. Phys. Lett.} {\bf 22} (2005) 1855).     

Solving the atmospheric scattering optical transfer function using the multi-coupled single scattering method

The atmospheric scattering optical transfer function （OTF） is solved by applying the multi-coupled single scattering （MCSS） method to the three-dimensional radiative transfer equation （RTE） under the periodic ground condition. This approach is a direct hit to the atmospheric scattering OTF using the same original context of modulation transfer function （MTF） measurement, i.e., images of sinusoidal grating at different spatial frequencies. Both the amplitude and phase shift of the OTF at various zenith and azimuth angles can be obtained at an arbitrary spatial frequency.     

非线性波方程求解的新方法

从Legendre椭圆积分和Jacobi椭圆函数的定义出发，得到了新的变换，并把它用于非线性演化方程的求解.用三个具体的例子，如非线性Klein-Gordon方程、Boussinesq方程和耦合的mKdV方程组，说明了具体的求解步骤.比较方便地得到非线性演化方程或方程组的新解析解，如周期解、孤子解等. 关键词： Jacobi椭圆函数 非线性方程 周期解 孤子解     

Linear double universal Grassmann manifold method for the stationary axisymmetric vacuum gravitational field equations

Nagatomo's universal Grassmann manifold scheme is extended to a double form, which is used to find the exact solutions of the stationary axisymmetric vacuum gravitational field equations. Some new results are given.     

实现散射场强整形的微散射体阵列逆向设计方法

本文提出一种基于全介电微散射体的散射阵列结构逆向设计方法,用以实现散射电场强度整形.该方法基于空域傅里叶变换与角谱变换,从给定目标区域处期望实现的散射场强分布出发,逆向求得所需的感应源,再利用电磁感应源理论,逆向设计微散射体阵列,且只需通过解析计算便能够快速地求取出微散射体阵列的电磁参数值分布.基于提出的逆向设计方法,文中提供了三维情况下的具体算例,实现了给定方形面目标区域的散射场强整形.理论计算结果与全波仿真结果符合良好,表明本文提出的逆向设计方法具有可行性与有效性.     

高对比度目标的电磁逆散射超分辨成像

提出了一种适用于高对比度目标的超分辨成像方法,通过结合对比度源反演方法与基于轨道角动量的超分辨技术,实现对高对比度目标的超分辨成像.首先采用基于轨道角动量的成像方法求解出对比度函数,将其作为对比度源反演方法的迭代初值,虽然初值结果与实际目标相差较大,但是由于初值中已经包含了关于目标的倏逝波信息,再利用这个初值开始迭代便可以得到超分辨重建结果,这种方法具有一定的抗噪声能力.本文研究表明,为了实现超分辨成像,一方面需要将目标对应的倏逝波信息转化到测量数据中,另一方面还要保证成像算法能够充分利用这些信息.本文所引申出的关于超分辨信息的概念对于逆散射超分辨成像的研究具有一定的借鉴意义.     

Multi-coupled single scattering method of solving vector radiative transfer equations

<正>A new method of multi-coupled single scattering(MCSS) for solving a vector radiative transfer equation is developed and made public on Internet.Recent solutions from Chandrasekhar’s X-Y method is used to validate the MCSS’s result,which shows high precision.The MCSS method is theoretically simple and clear,so it can be easily and credibly extended to the simulation of aerosol/cloud atmosphere’s radiative properties,which provides effective support for research into polarized remote sensing.     

Relevance vector machine technique for the inverse scattering problem

A novel method based on the relevance vector machine(RVM) for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.The nonlinearity is embodied in the relation between the scattered field and the target property,which can be obtained through the RVM training process.Besides,rather than utilizing regularization,the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output.Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy,convergence,robustness,generalization,and improved performance in terms of sparse property in comparison with the support vector machine(SVM) based approach.     

非线性波方程尖峰孤子解的一种简便求法及其应用

根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH（Camassa-Holm)方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解. 关键词： 非线性波方程 尖峰孤子解 待定系数法     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.     

一种新的求解脑磁逆问题的搜索方法

给出一种新的求解真实头模型下脑磁逆问题的搜索方法.通过不同位置的源的相互关系，由上一个搜索源的计算结果通过简单计算，直接得到下一个搜索源的结果，避免了繁琐耗时的边界元积分方法，简化了求解过程，提高了求解速度. 关键词： 脑磁图 逆问题 搜索方法     

New multi—soliton solutions and travelling wave solutions of the dispersive long—wave equations

Using the extended homogeneous balance method,the (1 1)-dimensional dispersive long-wave equations have been solved.Starting from the homogeneous balance method,we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation.Usually,we can obtain only a type of soliton-like solution.In this paper,we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.     

X—射线荧光分析散射幂函数法的原理及其应用

本文在较宽在基体原子序数变化范围内研究了非相干散射随基体吸收系数的变化规律,发现存在一种幂函数关系,用射内标法所假定的反比关系仅在较窄的轻元素范围内存在,实验证实了这种理论规律的存在。提出了用康普散射幂函数法校正基体吸收效应的新方法。列举了幂函数法在地质样品中的锶的测定实例,证明了该法在宽的基体组成范围内比传统的散射内标法适应性强。     

A deep learning method for solving high-order nonlinear soliton equations

We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higher-order nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg–de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.