Soliton

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另一方面梁的轴向应变的表达式也会因变形大小的不同而采用不同的表达式比如小变形时应变而当考虑大变形时可能采用的应变表达式就是进而得到的梁的振动方程将会是一个含有高度非线性项的偏微分方程组
非线性动力学入门
张新华
西安交通大学 工程力学系 2011 年 07 月
前 言
─1687 年，牛顿(Isaac Newton, 1643 ～ 1727)发表了《自然哲学之数学原 理》(Mathematical Principles of Natural Philosophy)，标志着经典力学(亦即牛 顿力学)的正式诞生。牛顿力学主要研究自由质点系的宏观运动规律。 ─1788 年，拉格朗日(Joseph Louis Lagrange, 1736 ～ 1813)发表了分析力 学教程(Analytical Mechanics)，标志着拉格朗日力学的诞生。Lagrange 力学属 于分析力学的主要内容之一，在位形空间中研究带有约束的质点系动力学。 ─1833 年，哈密尔顿(William Rowen Hamilton, 1805 ～ 1865)对 Lagrange 力学进行了改造，引进了相空间(2n 维空间)，对系统内在的对称性(辛对称， Symplectic)进行了刻画。狭义上的哈密尔顿力学只适用于保守系统，而广义 的哈密尔顿力学在适用于非保守系统。哈密尔顿力学也属于分析力学的主要 组成部分。在此后发展起来的量子力学中 Hamilton 力学发挥着巨大的作用。 目前在天体力学、计算 Hamilton 力学，量子力学，甚至弹性力学(即所谓的 辛弹性力学)中哈密尔顿力学依然发挥着重要作用。 ─1927 年，Birkhoff(George David Birkhoff, 1844 ～ 1944)发表了“动力系 统”(Dynamical Systems)，标志着 Birkhoff 动力学的正式问世。Birkhoff 动力 学建立了研究非完整力学的框架。 ─1892 ～ 1899， 彭加莱(Henri Poincaré, 1854 ～ 1912)发表了三卷本的“天 体力学中的新方法”(New Methods of Celestial Mechanics)，系统性地提出了 研究动力学系统的定性方法，即几何方法。经典力学的目标之一就是设法求 得系统的解析解，而 Poincaré意识到对于大多数非线性系统而言，求其解析 解是不可能的，而必须发展新的研究方法。他超越了他的时代，极富远见地 预测到了非线性系统混沌现象(系统的解对初始条件具有极端敏感依赖性)的 存在。更为重要的是，Poincaré开创了研究非线性动力系统的几何方法，当之 无愧地被誉为非线性科学之父，其影响是划时代的。 ─1892 年，李亚普诺夫(Aleksandr Mikhailovich Lyapunov, 1857 ～ 1918)在 他的博士论文“运动稳定性的一般问题”(General problem of the stability of motion )中，系统地探讨了非线性动力学系统的稳定性问题。他提出了两种研 究稳定性的方法：李亚普诺夫第一方法(间接方法)和李亚普诺夫第二方法(直 接方法)。他从代数角度出发，对动力学系统的研究开创了一个崭新的领域。 彭加莱与李亚普诺夫，前者从几何角度，后者从代数角度，开拓了非线 性科学的研究疆域和研究手段。 ─1963 年，Lorenz(Edward Norton Lorenz, 1917 ～ 2008)发表了“确定性 非周期流”(Deterministic Nonperiodic Flow)的论文，认为大气系统的性态对 初值极为敏感，从而导致准确的长期天气预报是不可能的。该文标志着人类 首次借助于计算机发现了混沌(Chaos)现象的存在。 ─1757 年，欧拉(Leonhard Euler, 1707 ～ 1783)发表了压杆稳定性的论 文，首次探讨了力学系统的分岔现象。作为分岔理论重要分支的突变理 论(Catastrophe Theory)则主要由法国数学家托姆(René Thom, 1923 ～ 2002)于 上个世纪 60 年代创立，由齐曼(Christopher Zeeman，1925 ～)在 70 年代大力 推广普及。 ─1834 年，英国的罗素(John Scott Russell, 1808 ～ 1882)骑着马在 Union 运河上散步时，发现了现在称之为孤立波(又称作孤波，Solitary wave)的 i

Soliton Systems Whitepaper Integration Between the Soliton Zao VMS Plus and Milestone XprotectMobile SurveillanceAndRemote Live Video StreamingContentsIntegration between the Zao VMS Plus and Milestone XProtect® (3)Purpose of the paper (3)Summary (3)Benefits (5)User case Scenario (5)Application Examples of the Solution: - (6)Soliton – Transmission End (7)Soliton – The Receiving End (7)Milestone Systems – Requirements and Install (7)Milestone XProtect Installation (8)Installation of Zao VMS Plus (MGW and Web Management) (13)Where to Buy (15)Support (15)More Information (15)Online Product Information: (15)Integration between the Zao VMS Plus and Milestone XProtect® Purpose of the paperThis white-paper describes the integration between the Zao VMS Plus from Soliton Systems and the Xprotect® VMS from Milestone Systems. The live streaming Smart-telecaster transmission units of Soliton are used to compress and live stream video from a mobile camera in a remote location, and the Video Management System (VMS) platform from Milestone Systems is used to display, record and manage the video stream(s) back at an operational centre.This paper describes what is required to set up an integration, some user case scenario’s and a summary of the benefits.SummarySoliton Systems is a Japanese technology company specialising in IT security and outdoor mobile video surveillance products. Within the outdoor mobile surveillance element of Soliton, the Smart-telecaster range of products consists of:•2x H.265 (HEVC) hardware video encoder products:o Zao-S (up to 3x SIM cards and maximum bit rate of 5 Mbps)o Zao (up to 6x SIM cards and maximum bit rate of 10 Mbps)They are typically deployed in a remote or moving location with an external video camera and can live stream over multiple 5G / 4G / PS LTE connections to a receiving platform at the destination (typically a command centre). They can live stream from action-cams on a person or fromcameras situated on vehicles, boats, trains, helicopters and/or drones.• 2 x Live Streaming Apps for Smartphones:o Zao App for Androido Zao App for iOSThe Zao App won the Airbus Critical App Award Belgium 2018 for deployment on their TactilonDabat, which is the world’s first smartphone and full TETRA radio in one device. Zao Appsupports Full HD, 25fps, H.265 & H.264 codec, AES 256-bit encryption, authentication, GPSinformation, two-way audio.• 2 x separate software receiving (“decoder”) products for VMS integrationo HD View (1 channel or 4 channel software products installed on Win10 platform)o Zao VMS Plus (Virtual machine platform can be installed on-premises or in cloud) used for VMS systems – supports up to 12 x live stream channels to create up to 12 x RTSP H.265ONVIF compliant streams.The decoders are typically placed at the receiving destination and are used it to either create an IP video stream (RTSP, RTMP or NDI), or to create an uncompressed HD-SDI video stream forbroadcast purposes. Xprotect utilises an IP ONVIF compliant RTSP H.265 stream.The mobile encoders are used to live stream from a mobile camera. They utilise H.265/HEVC to compress the video using the latest HEVC technique. They can create a highly reliable connection by “bonding” up to 3 simultaneous SIM cards from 3 different cellular providers on the Zao-S (or up to 6 different network providers on the Zao) which are then used simultaneously to transmit.Where 4G connection may be weak or unreliable, by combining all the telco network providers as a single connection, this mitigates the risk of relying on one single provider with the benefit of combining all the bandwidth across all the connections for increased speed and reliability.The streams are fully encrypted using AES256, and in conjunction with VMS Plus at the receiving end, can provide a fully ONVIF compliant live stream to XProtect.Milestone Systems is a Danish company that develops the XProtect® Video Management System (VMS) to activate, display, monitor and record live video feeds, typically placed within an operational or command centre. Traditionally they are camera agnostic utilising ONVIF compliant fixed surveillance cameras’. Milestone Systems works with a range of partners to provide an eco-system around their products consisting of camera manufacturers, video storage manufacturers, analytical vendors, door access control manufactures and more recently Artificial Intelligence (AI) developers which includes video analytics. Traditional uses of Milestone’s Xprotect® VMS is for monitoring fixed surveillance cameras. Soliton Systems is now a certified partner of Milestone Systems providing a new concept in terms of providing live streaming from mobile or roaming cameras that could be body-worn cameras, placed in vehicles, motorbikes, video surveillance vans, drones, helicopters, boats, planes or even on dogs.Official support began end of August 2018 when the Soliton solution was included in Milestones Xprotect device pack version 9.9.BenefitsCompanies do not want to buy products, they wish to buy solutions which are proven, certified, fit-for-purpose and supporting open recognisable standards for interoperability.The solution being offered from Soliton is the Zao-S or Zao (hardware encoders connected to the camera), or live streaming app on a smartphone, in conjunction with the Zao VMS Plus in combination with Milestone Xprotect VMS system.The Zao-S has multiple technical benefits when used in the Public Safety and Law Enforcement domain: -•H.265 HEVC encoding is 50% more efficient than traditional H.264 encoding requiring half the bit rate for transmission•The units are the smallest and lightest H.265 HEVC mobile encoders globally available•The units can bond together up to 3 x SIM cards making them highly reliable even when signal strength is low or non-existent on some cellular networks•Real Time bonding, known as RASCOW, optimizes video quality based on available total bandwidth across all available 5G / 4G / PS LTE networks and adjusts video accordingly in realtime in a dynamic situation such as a high-speed pursuit.•Can be utilised in low cellular coverage or crowded places even when there is competition for network availability•Future proofing for 5G•The units support AES256 encryption•Fully ONVIF compliant•Low latency – typically 700ms from camera to VMS and as low as 240ms•Browser based management of all units in field•Working with any drone or any camera to provide live feeds from the field to HQ for live analyticsUser case ScenarioUtilised on a global stage with many law enforcement, first responder and emergency services, the Zao-S allows instant video live streaming from remote mobile situations such as body worn actions cams, police surveillance vehicles, coast guard, fire departments used within drones, helicopters and even in some cases live streaming from dogs. This is achievable by the miniature device utilising multiple 4G connections simultaneously to live stream video reliably back to a command centre in full HD (1080p) with minimal latency.As a user case scenario, the Zao-S is already deployed by the Tokyo Police in conjunction with Milestone Xprotect® and was originally used as a Public Safety tool for the Tokyo marathon. There is a case study that describes the Tokyo Police and Milestone user case in more detail here: -https:///case-study-news-gathering-smart-telecaster-live-news-gathering-2/ Soliton also have another major European Police force using multiple Zao-S with a Milestone Xprotect® VMS system in live operational duties where it is being utilised for special operations, raids and covert operations.If you wish to read more about the advantages of mobile surveillance with Soliton, then please read this article: https:///insights/mobile-surveillance-live-stream-cameras-drones-co-14303-ga.1524220758.htmlApplication Examples of the Solution: -Components of the Solution:Field Side1) Camera: In case of using ZAO or ZAO-S, any camera with HDMI or SDI output can be used. Drones with HDMI output, body-worn action cameras (helmet cameras), hidden cameras and/or in vehicle cameras.2) Soliton Transmitter: ZAO / ZAO-S are Soliton’s bonding encoders that can use multiple network connections at the same time. ZAO App is the smartphone app solution uses the smartphone’s camera. All transmitter solutions use H.265 codec and Soliton’s RASCOW transmission technology, therefore, all Soliton transmitters have two-way audio, encryption, GPS and error correction technologies.# important note: Soliton’s transmission system is a point to point and fully encrypted solution.HQ Side3) Soliton Receiver: Soliton’s receiver side is a virtual machine with software packages (VMS Plus) with the main goal of converting Soliton’s RASCOW protocol to RTSP and communicate with VMS server via ONVIF. Soliton’s receiver solution is ideally located in the same local network as Xprotect® VMS server.4) Milestone Xprotect® VMSSoliton – Transmission EndThe live streaming side of the solution consists of: -•Camera (this does not need to be ONVIF complaint given the Zao-S provides thisfunctionality) – 1080i/1080p/720p/….•Zao-S•Up to 3 Dongles with SIMs – see here for supported dongles – each configuredwith the APN setting of the SIM (it is also possible to use Wi-Fi or Satellite to live stream)•Option – Zao Controller for iPhone/Android (Management tool)The Zao-S is put together as in this video.Soliton – The Receiving End•Zao Cloud VMS PlusThe Zao VMS Plus system consist of two major elements: -1)Media Gateway – to receive the RASCOW stream and pass through an H.265video stream via RTSP/ONVIF to a VMS server.RASCOW (Real-time Auto Speed Control based On Waterway model) is Soliton’snetworking protocol to optimise the best video quality based on the multiple networkavailability. It allows the units to operate effectively even when there is limited bandwidthwhile maintaining low latency.Sub blocks consist of: RTMP server, End Point Server and Receiver Software (see diagramabove).2) Web Management – Management database and user interface to remotely manage allthe units in the field.Both components of VMS Plus stated above are provided by Soliton as an ESXi VMappliances.Sub blocks consist of: Comm Post and Web Management (see diagram above). Milestone Systems – Requirements and InstallRequirements: -•Xprotect Smart Client•Xprotect Recording ServerMilestone XProtect versionThe following is high level summary of what is required. Note a more in-depth installation manual is available from Soliton detailing the installation.There are several different Milestone VMS products in the XProtect range, starting at the XProtect Essential+ (single site, free version) all the way to the XProtect Corporate (multi-site, scalability, etc) More Information can be found at the following URL:https:///solutions/platform/video-management-software/•XProtect Essential+ - Single site, up to 8x cameras•XProtect Express & Express+ - Single site, up to 48x cameras, XProtect add-ons•XProtect Professional & Professional + - Multi-site, unrestricted number of cameras, XProtect add-ons & scalability•XProtect Expert - Multi-site, unrestricted number of cameras, XProtect add-ons, scalability, redundancy & hardware acceleration in recording server•XProtect Corporate - Multi-site, unrestricted number of cameras, XProtect add-ons, scalability, redundancy, hardware acceleration in recording server & distributed operationMilestone XProtect InstallationThe Milestone XProtect products can be downloaded at the following URL:https:///support/resources/download-software/(For the purposes of this document XProtect Essential+ 2018 R3 free version was used, current version available is XProtect 2019 R1)After installation is complete select Restart Computer.The installation process will resume automatically after the reboot and once completed the computer will need to be restarted again.The final installation menu displays the components that have been installed.The installation has now been completed and the configuration process begins.On the first menu, all the fields should be left blank and Continue.Over the next menus, leave the default and Continue.Once the final configuration menu appears, just press Close.The basic configuration of XProtect VMS has now been completed and the setup can begin.It is important to note that before a live stream can be received in the Milestone XProtect Smart Client a Recording Server will have to be configured through the XProtect Management Client.The Management Client has a range of options and configuration settings that will allow anything from a Basic to an Advanced Setup, depending on the needs of the user/customer and allows for customization.For the purpose of this paper and since a Zao-S H.265 encoder will be used to transmit a live stream, the following steps reflect the configuration of a Recording Server as well as the addition of the Zao-S hardware to the Milestone VMS platform and ultimately receiving the live stream on the Milestone XProtect Smart Client.Recording Server Configuration & adding Zao-S hardwareOn Site Navigation, select Servers, Recording Servers and Add Hardware (same as image below).Once the Add Hardware menu shows, select Manual and Next.You will then be prompted to specify Username & Password which should be left blank by default and the next.At the driver selection menu all checked options should be removed and only ONVIF should be selected.The IP Address of the VMS+ (Media Gateway) server and the port to receive will need to be added. (Refer to VMS+/Media Gateway setup and requirements)The available port range used to distribute video to XProtect is between 40011-40121 and for each port on the Milestone side there’s an equivalent port on the VMS+ platform with range between 20010-20120.Each side has 12 ports available with each one corresponding to a livestream channel to a total of 12 channels at this time and more are expected to be added in the future. For each added Zao-S encoder, a new available port will have to be assigned.Port assignment should look as follows:Port information on XProtect VMS+ Endpoint port information40011 2001040021 2002040031 2003040041 2004040051 2005040061 2006040071 2007040081 2008040091 2009040101 2010040111 2011040121 20120It is important to add that when switching the output destination port of the video in the XProtect side, the VMS+ Endpoint port should be changed to matching port according to the table above. (Refer also to VMS+/Media Gateway setup and requirements)Once the registration is successful there should the IP Address, Port, Hardware Model information and the Status will show as Success indicating the Zao-S encoder was successfully added.In order to enable the device, following options should be selected:•Hardware•Camera 1,•Microphone port 1,•Speaker port 1Once completed, it will be visible on the XProtect Management Client the recently added fields our Recording Server.A green triangle mark should be visible on all the added fields indicating that images are now being received on the Milestone VMS platform.In order to view the configured stream, it’s time to open XProtect Smart Client which will be the receiving end of our live stream.For first-time users a new View will need to be added by performing the following steps:Select Views -> Default group - > Default view group -> Add View - > 16:9 -> 1+3 and selectSetup to complete adding the View.On the left-hand side, the Zao-S (which will show under Cameras) will be visible has Soliton System IP Camera and a simple Drag and Drop to the Main View will bring the livestream onto the Smart Client. Additional manuals & guides for the XProtect VMS products can be found at:https:///support/resources/download-software/?prod=1419&type=13&lang=27 Installation of Zao VMS Plus (MGW and Web Management)Please note installation of VMS Plus would be installed by Soliton personnel or by Soliton trained partners.Both components of VMS Plus (Zao Media Gateway and the Web Management) are provided by Soliton as two separate ESXi VM appliances and are installed in virtualised environments. It is possible to install both components on a single machine or two separate machines and can be on-premise, or can be installed within a Cloud environment such as Azure.Hardware Requirements:VMware vSphere Hypervisor ESXi 6.7 environment (Build 8169922)8Core CPU, 32GByte Memory, 500GB HDDUSB Memory (For copying license file to VM)2 VM image files for Media Gateway and Zao Web Management*Certification file for Zao Web Management*License file for Media Gateway**provided by SolitonExample Spec (May 2019): -o HP DL360 G10o Single 4114o32G RAMo 2 x 1TB RAID1o OPTICALo Dual PSUo MS Win 2016 ROKThe Web Management solution includes the “Com Head” which effectively manages the network connections and the interface with the Zao Web Management solution. The Zao Web Management is normally a hosted service in an open network environment, but it is normally installed alongside the VMS plus solution in closed networks such as those used by many law enforcement agencies.The Zao web management allows the configuration of both the receiver and the transmission elements where settings can be administered, and a preview of the network availability and video is available. The web management is browser based.As a summary, the Zao VMS Plus product will assemble the video arriving from all the separate network connections whether it be via multiple 3G/4G connections, WiFi and/or satellite, translate from RASCOW/H.265 to RTSP/H.265 and decrypt the stream to an ONVIF complaint stream that can be used asan input to Xprotect. Normally with a latency from the mobile camera to the input of Xprotect is less than a second, typically 700ms.A user manual is available that details the installation procedure for Zao VMS Plus.Cloud Providers that can be utilized: Customer preference (AWS and Azure tested)Where to BuySoliton Systems sell through a range of distributors, System Integrators, Resellers and other partners across the globe. Please contact us for more information or see our list of resellers.SupportPlease see our support page for a list of manuals and other useful video and documentation. Here is also an email address to request support if required.More InformationOnline Relevant case studies, videos, blogs: -Milestone & Soliton Systems - Japanese Police Case Study (text)Public Safety Video Using Zao-S (Video)Milestone and Soliton – Sales Value Proposition (Video)Drones and Wild Fires Blog (text)Online Product Information:Soliton – specialist in mobile live streaming for mobile surveillance and outside broadcast•Used by special operations, first responder, covert operations, drones, police pursuits, helicopters to live stream instantly over multiple 4G networks back to a command centre.•Zao-S is smallest H265 encoder in the world at only 400 grams for transmission over multiple 5G / 4G / PS LTE networks simultaneously – very reliable even at low bit rates.•Latency as low as 700ms back to command centre and now looking at lower latency solutions from 50ms.•Fully encrypted using AES256.•Fully ONVIF compliant allowing integration into VMS systems such as Milestone that is in use by many law enforcement organisations.•Receiving end (decoding platform either HD View or Zao Media Gateway) can be securely on-premise with no cloud infrastructure – with encryption all the way.•Receiving end (Zao Media Gateway) allows up to 12 channels and can create an RTMP/RTSP stream that integrates with Video Management Systems (VMS) that are typically used forfixed surveillance systems.•Option to display streams on a map for quick decision-making capabilities. E.g. pursuit vehicles and clearly seeing where to deploy additional officers/agents on a map in real time.•Remote cameras are assumed to be HD-SDI or HDMI. If they are using IP cameras, we may have a product coming that could be of interest though all action and mobile cams I know ofdo not yet support IP output.•Potential to control fixed PTZ cameras via a serial port on Zao-S.•Full browser management capability to control all units in the field with GPS tracking.More information: -•Transmitter - Zao (up to 6 SIM cards) - /products/smart-telecaster-zao/•Transmitter - Zao-S (up to 3 SIM cards) – new miniature encoder, weighing only 400g with internal battery – /products/smart-telecaster-zao-s-2/•Receiver – Zao VMS Plus supports up to 12 channels and can be hosted on an Azure platform or On premise. To create ONVIF complaint H.265 streams for a VMS.•Alternatively HD-View software decoder that works on standard win 7 / win 10 platform that works with both Zao, Zao-S & ML Cam - /products/stc-hd-view/•and ML Cam (iPhone and Android streaming app) - /products/stc-ml-cam/•Full SIM cards and dongles can be provided. For HD View you only need the decoding hardware (Win 7 or win 10 server min 16GB RAM) and Blackmagic Decklink card if using HD-SDI workflows. (Decklink card not required for IP workflows – RTMP/RTSP/NDI/Milestone).The decoding hardware requires an external facing (global) IP address.More Information: Please contact Soliton sales team on: ********************。

孤立子模及其推广的开题报告一、研究背景：孤立子（Soliton）是一种特殊的非线性波，它在传播过程中可以保持其形状和速度不变，并且没有能量损失。

孤立子最早出现在Korteweg-de Vries（KdV）方程的解中，被认为是一个数学奇迹。

而后，随着对孤立子的研究不断深入和拓展，孤立子在电磁场、物理、生物、力学等领域中得到了广泛应用，成为了一个专门的研究方向。

在真实的自然界中，很多现象都可以用孤立子理论描述，如水波的波峰、山峰、物质波等。

传统的孤立子模型是基于KdV方程的解构造，并没有广泛适用于实际情况。

为了更好地描述真实世界中的现象，人们对孤立子模型的研究进行了推广和拓展。

在这方面，研究人员提出了各种新的孤立子模型，如：变系数KdV模型、多孤立子模型、Painlevé模型等。

这些模型对实际应用和理论研究具有重要意义，本文将探讨这些孤立子模型的推广及其应用。

二、研究目的：1.深入探究孤立子的特点和发展历程，了解孤立子模型的基本原理和构造方法。

2.分析传统孤立子模型存在的研究局限性，并对其进行扩展和推广，提出相应的新孤立子模型。

3.探讨新孤立子模型的数学特征、解析性质和应用前景，为实际问题的解决提供理论依据和数值方法。

4.具体应用领域：以微纳米系统和高速信息通讯技术为例，探究孤立子模型的应用，研究孤立子在这些领域中的数学建模和实际应用。

三、研究内容和进度：本课题的具体研究内容包括：1.简要介绍孤立子的基本特点、历史渊源和研究现状，阐述其在实际问题中的应用前景。

2.对经典孤立子模型进行分析，指出其存在的研究局限性，并提出新的孤立子模型，包括变系数KdV模型、多孤立子模型、Painlevé模型等。

3.分析新孤立子模型的数学性质，如可积性、解析性质等，并研究相应的数值方法和实现方式。

4.以微纳米系统和高速信息通讯技术为例，探究孤立子模型的应用。

具体包括：建立系统动力学模型，分析孤立子的产生和演化规律，对系统进行数值模拟和实验验证，并对模型的稳定性和可控性进行分析。

solid词根词缀记忆法
"solid"是一个常见的英语词根，表示坚固、稳固和完整。

以下是一些常见的以"solid"为词根的词缀及其含义：
1. soli-：单一、单独（solo单独的、一个人的）
- solitary (孤独的、独居的）
- solitaire (单人棋类游戏）
2. -id ：性质、特征（identity身份）
- solid (固体的、坚固的)
- fluid (流体的、液体的)
3. sol-: 太阳（sun太阳）
- solar (太阳的、太阳能的)
- parasol (太阳伞、遮阳伞)
4. solv-：溶解、解决（solve解决）
- dissolve (溶解、解散)
- solvent (溶剂、有解决能力的)
5. solit- ：独自、单独（solitude孤独）
- solitary (孤独的、独居的)
- soliton (孤立子)
这些词缀可以帮助我们记忆、理解和推测与"solid"相关的单词的含义。