In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本論文建立了系統(tǒng)的暗孤子直接微擾方法，在對前人關于暗孤子微擾方法的錯誤以及亮孤子直接微擾方法的本質作了充分的分析后中文字幕第二一区，認識到引入平方Jost解的伴隨解和證明完備性是問題的關鍵人人干人人操人人舔人人摸，撇開過去亮孤子情況首先引入伴隨算子的非必要作法，直接從平方Jost解與其伴隨解的內積在連續(xù)譜時正比于δ函數(shù)這一正交性要求出發(fā)野花香视频在线观看6，找出了伴隨解国内小视频，同時得出了應有的伴隨算子，在考慮到約化變換性后日韩成人成色在线播放网站，得到了暗孤子情況的平方Jost解的完備性的正確表述su4.com，并在單個暗孤子的情況利用平方Jost解的顯式直接驗證了它的正確性。

It also researches the application of variational method to solve the perturbation function in the energy principle.

本文還探討了變分方法在求解能量原理中的擾動函數(shù)的應用2020年精品黄色视频。

The output chaotic sequence through the perturbation function distributes uniformly in the whole state space.

經(jīng)過擾動函數(shù)的輸出混沌序列均勻分布在整個狀態(tài)空間中可以看视频的黄色网站。

In Chapter 1, the resonant phenomena of the NEAs' movement are introduced, briefly expounded the concepts of the mean and secular resonances as well as the way of extracting the resonant parts of the expansion of the perturbation function, still well established the corresponding resonant models.

在第一章中，介紹了近地小行星運動中的共振現(xiàn)象AV片在线观看网址大全，扼要地闡述了軌道共振和長期共振的概念久久va中文字幕影视、共振項的析取方法以及建立了相應的共振模型。

Instead of the empirical direct substitution method used in former harmonic ex- pansion method for the generation of perturbation base function s,a more rigorous 1~or- der perturbation method was proposed to generate the perturbation base function s.

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In chapter four, we developed a direct approach for soliton perturbation based on the Green function, This approch get rid of the proof of orthognality for eigenfunctions in a direct approch for soliton perturbation developed by Yan Jiaren etal.

第四章，發(fā)展了一種基于格林函數(shù)的孤子微擾理論天堂AV在线播放最新版，克服了顏家壬教授微擾直接法中本征函數(shù)正交性證明的困難精品射射射福利一区。

In part two, the optical spatiotemporal pattern in ring optic cavity is investigated. Using delay feedback with spatial perturbation method, the system shows roll, square, hexagon, homocentric circle,"honeycomb"and"snowflower" pattern with different spatial perturbation functions. Different patterns can be coexist and compete each other with the same perturbation function, which is the new character of this optical system with delay feedback.

第二部分，利用延時反饋的空間微擾方法研究了環(huán)形腔中二能級介質的光學時空斑圖的控制免费黄色在线啊～啊～，在不同的微擾函數(shù)作用下亚洲国产一区二区三区青草影视，出現(xiàn)了滾筒狀、四方形国产妇女AAAAAAAA手机看片、六角形鸥美色精品在线播放、蜂窩狀又污又黄又爽的网站、同心圓以及"雪花"狀等不同的斑圖，并且在相同的微擾函數(shù)下出現(xiàn)了不同斑圖之間的競爭成年人在线观看，這種競爭是我們發(fā)現(xiàn)的這一具有空間微擾的延時反饋非線性光學系統(tǒng)光學斑圖的新特征国产一级AA片有黄有粗毛片。

As a result of conservative perturbations, the first order Melnikov function for a perturbed system is identically equal to zero, so the second order Melnikov function has to be considered. The perturbation parameters which make no use in the first order Melnikov function may be important in the second order Melnikov function.

此時一階Melnikov函數(shù)恒等于零，必須考慮二階Melnikov函數(shù)日本女优一区二区，而在一階Melnikov函數(shù)中不起作用的擾動參數(shù)在二階Melnikov函數(shù)中卻起著非常重要的作用，因此擾動部分極為復雜欧美性影片在线观看。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

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In part two, the optical spatiotemporal pattern in ring optic cavity is investigated. Using delay feedback with spatial perturbation method, the system shows roll, square, hexagon, homocentric circle,"honeycomb"and"snowflower" pattern with different spatial perturbation functions. Different patterns can be coexist and compete each other with the same perturbation function, which is the new character of this optical system with delay feedback.

第二部分，利用延時反饋的空間微擾方法研究了環(huán)形腔中二能級介質的光學時空斑圖的控制jizz女，在不同的微擾函數(shù)作用下国模吧首页，出現(xiàn)了滾筒狀、四方形免费看污视频的网站、六角形久久99久久久久久精品、蜂窩狀、同心圓以及&雪花&狀等不同的斑圖久久精品大全，并且在相同的微擾函數(shù)下出現(xiàn)了不同斑圖之間的競爭国产黑丝无码，這種競爭是我們發(fā)現(xiàn)的這一具有空間微擾的延時反饋非線性光學系統(tǒng)光學斑圖的新特征。