The periodic solutions for coupled integrable dispersionless equations

By using the Jacobi elliptic-function method, this paper obtains the periodic solutions for coupled integrable dispersionless equations. The periodic solutions include some kink and anti-kink solitons.

N-soliton solution of a coupled integrable dispersionless equation

A new coupled integrable dispersionless equation is presented by considering a spectral problem. A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems. As an application, the N-soliton solution of the coupled integrable dispersionless equation is explicitly given.

N-Rotating Loop-Soliton Solution of the Coupled Integrable Dispersionless Equation

In this paper, we investigate the Rotating N Loop-Soliton solution of the coupled integrable dispersionless equation (CIDE) that describes a current-fed string within an external magnetic field in 2D-space. Through a set of independent variable transformation, we derive the bilinear form of the CIDE Equation. Based on the Hirota’s method, Perturbation technique and Symbolic computation, we present the analytic N-rotating loop soliton solution and proceed to some illustrations by presenting the cases of three- and four-soliton solutions.

Conservation Laws and Analytic Soliton Solutions for Coupled Integrable Dispersionless Equations with Symbolic Computation

Under investigation in this paper are two coupled integrable dispersionless (CID) equations modelingthe dynamics of the current-fed string within an external magnetic field.Through a set of the dependent variabletransformations, the bilinear forms for the CID equations are derived.Based on the Hirota method and symboliccomputation, the analytic N-soliton solutions are presented.Infinitely many conservation laws for the CID equationsare given through the known spectral problem.Propagation characteristics and interaction behaviors of the solitons areanalyzed graphically.

New Exact Solutions and Special Coherent Structures for Coupled Integrable Dispersionless Equation

用改进同类的平衡方法，我们少些为联合 integrable 分散获得新准确答案方程。根据这些准确答案，我们由适当地选择任意的功能发现一些新有趣的协调结构。

New Exact Solutions of (1+1)-Dimensional Coupled Integrable Dispersionless System

这份报纸使用 exp 功能方法，它原来被建议发现新准确旅行非线性的进化方程的波浪答案，到 Riccati 方程，和这个方程的一些准确答案被获得。基于 Riccati 方程和它的准确解决方案，我们与二个任意的函数发现新、更一般的可变分离解决方案(1+1 ) 维的联合 integrable 无分散的系统。作为一些特殊例子，一些新答案能堕落进在开的文学报导的可变分离答案。由合适在我们的答案选择二独立变量 p (x) 和 q (t) ，扁平盆的 soliton，拱门盆 soliton，和有平面的东西 soliton 的歼灭现象被讨论。

Soliton Solutions to Coupled Integrable Dispersionless Equations

In this paper,by introducing a new transformation,the bilinear form of the coupled integrable dispersionless(CID) equations is derived.It will be shown that this bilinear form is easier to perform the standard Hirota process.One-,two-,and three-soliton solutions are presented.Furthermore,the N-soliton solutions are derived.

Darboux transformation and exact multisolitons for a matrix coupled dispersionless system

We present a matrix coupled dispersionless(CD)system.A Lax pair for the matrix CD system is proposed and Darboux transformation is constructed on the solutions of the matrix CD system and the associated Lax pair.We express an N soliton formula for the solutions of the matrix CD system in terms of quasideterminants.By using properties of the quasideterminants,we obtain some exact solutions,including bright and dark-type solitons,rogue wave and breather solutions of the matrix CD system.Furthermore,it has been shown that the solutions of the matrix CD system are expressed in terms of solutions to the usual CD system,sine-Gordon equation and Maxwell-Bloch system.

Block(or Hamiltonian) Lie Symmetry of Dispersionless D-Type Drinfeld–Sokolov Hierarchy

In this paper, the dispersionless D-type Drinfeld–Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type.

Generating a New Higher-Dimensional Coupled Integrable Dispersionless System:Algebraic Structures,Bcklund Transformation and Hidden Structural Symmetries

The prolongation structure methodologies of Wahlquist-Estabrook [H.D.Wahlquist and F.B.Estabrook,J.Math.Phys.16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system.Based on the obtained prolongation structure,a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed.A Lie-Algebra representation of some hidden structural symmetries of the previous system,its Bcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived.In the wake of the previous results,we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation,which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.

Recursion Operators for Dispersionless KP Hierarchy

Based on the corresponding theorem between dispersionless KP(dKP)hierarchy and -dependent KP ( KP) hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding KP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail.

无色散KP系列与Dunajski方程系列的相容性

从一阶微分方程组的角度出发,证明了无色散KP系列的相容性.类似地,采取与无色散KP系列相同的方法,证明了Dunajski方程系列算子m和n的相容性.这两个相容性也是无色散KP系列和Dunajski方程系列的一个新定义.

一类无散射偏微分方程组的变换和精确解

将 3个非线性物理方程组通过近似约化 ,转化为一类无散射的偏微分方程组 ,然后通过变换 ,化为一阶拟线性双曲型方程。利用拟线性双曲型方程的解 ,得到无散射偏微分方程组的精确解。参

ON THE MODIFIED NONLINEAR SCHRDINGER EQUATION IN THE SEMICLASSICAL LIMIT:SUPERSONIC,SUBSONIC,AND TRANSSONIC BEHAVIOR

The purpose of this paper is to present a comparison between the modified nonlinear SchrSdinger （MNLS） equation and the focusing and defocusing variants of the （unmodified） nonlinear SchrSdinger （NLS） equation in the semiclassical limit. We describe aspects of the limiting dynamics and discuss how the nature of the dynamics is evident theoretically through inverse-scattering and noncommutative steepest descent methods. The main message is that, depending on initial data, the MNLS equation can behave either like the defocusing NLS equation, like the focusing NLS equation （in both cases the analogy is asymptotically accurate in the semiclassical limit when the NLS equation is posed with appropriately modified initial data）, or like an interesting mixture of the two. In the latter case, we identify a feature of the dynamics analogous to a sonic line in gas dynamics, a free boundary separating subsonic flow from supersonic flow.

Explicit solutions of nonlinear wave equation systems

We apply the （G＇/G）-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. We highlight the power of the （G＇/G）-expansion method in providing generalized solitary wave solutions of different physical structures. It is shown that the （G＇/G）-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.

Dbaur-穿衣法和一个耦合无色散方程(英文)

利用基于2×2矩阵(Dbar)-问题的推广穿衣法,研究了一个耦合无色散方程,进而利用Cauchy矩阵的性质导出其孤立子解.此外,还讨论了N-孤立子解的渐近行为.

具有三个位势的广义耦合无色散可积方程的多孤子解(英文)

利用具有三个位势的2×2矩阵谱问题的规范变换,给一个广义耦合无色散方程构造了一种新的N重达布变换.作为达布变换的应用,获得了该广义耦合无色散方程的N-孤子解.

用于可见光波段切趾成像的宽带消色差超表面滤波器

切趾在成像和光通信领域得到了重要的应用。传统的切趾方法基于相位或者振幅调制,存在工作带宽窄或者分辨力低的问题。本文提出了一种宽带消色差的超表面滤波器,可以在不损失空间分辨力的情况下实现切趾成像。通过该滤波器在整个可见光波段完成了几乎无色散的相位调制。仿真结果表明,超表面滤波器的聚焦效率是相位滤波器的两倍;其成像对比度可以提升至高斯滤波器的三倍。通过我们的方法,在400 nm到700 nm的可见光波段内,点扩散函数的旁瓣能被压缩到10^(-5)数量级,同时能够实现衍射极限甚至超衍射的分辨力。

一类无散射耦合的Korteweg—de Vries方程组的约化和精确解

将一类无散射耦合的Korteweg-de Vries方程组约化为一阶拟线性双曲型方程，并给出了它们之间的一种变换关系，然后利用拟线性双曲型方程的解，得到无散射耦合的Korteweg-de Vries方程组的精确解。

2005年8月24日磁暴主相期间亚暴过程的多卫星联合观测分析

本文根据OMNI、TC-2卫星、LANL系列卫星、Cluster星簇卫星(C1—C4)以及加拿大的8个中高纬地磁台站的观测数据,研究了2005年8月24日强磁暴(SYM-Hmin^-179nT)主相期间的强亚暴(ALmin^-4046nT)事件特征.该强磁暴在大振幅(IMF Bz min^-55.57nT)、短持续时间(~90min)的行星际磁场条件下产生,有明显的磁暴急始(SSC),强度较大且持续时间较短.发生在磁暴主相期间的亚暴发展的主要特征如下:亚暴增长相期间,C1—C4卫星先后穿越中心等离子体片;亚暴膨胀相触发后,在近地磁尾(X^-6RE)可观测到磁场偶极化现象;等离子体无色散注入区在亚暴onset开始后迅速沿经向扩展,但被限制在有限的经度范围;磁纬60°附近,Pi2地磁脉动振幅超过了100nT.膨胀相开始后,在中、高磁纬地磁台站可观测到负湾扰,近地磁尾可观测到Pi2空间脉动,中磁尾区域可观测到尾向流、磁重联以及O+/H+数密度比值在亚暴onset之后增大等现象.分析表明该强磁暴主相期间的强亚暴现象发生时序是自内向外:X^-6RE处TC-2观测到磁场偶极化(~09∶42∶30UT),同步轨道卫星LANL1994-084观测到等离子体无色散注入(~09∶44∶30UT),X^-17.8RE处C1观测到磁场重联(~09∶45∶30UT),由此推断该亚暴事件很可能是近地磁尾不稳定性触发产生,其发生区域距离地球很近.