rational differential equation 中文意思是什麼

rational differential equation 解釋
有理微分方程
  • rational : adj 1 理性的。2 推理的；有理性的；懂道理的，講道理的；合理的，合道理的；純理論的。3 【數學】有理...
  • differential : adj 1 差別的，區別的；特定的。2 【數學】微分的。3 【物、機】差動的，差速的，差示的。n 1 （鐵路不...
  • equation : n. 1. 平衡，均衡；平均，相等。2. 【數學】方程式，等式。3. 【天文學】（時）差；均分，等分。4. 【化學】反應式。
  1. Abstract : in this paper, we consider a class of irrational rumber which can be approximated by rational number at most exponental order ， applications are given in partial differential equation and dynamical systems

    文摘:文中考慮一類最多可以指數地有理逼近的無理數，並指出它們自然地存在於偏微分方程解析理論及動力系統中
  2. The second part, with the aid of many types constructive transformation and symbolic computation ( especially wu algebraic elemination method ), some topics in nonlinear evolution equation are studied, including exact solution ( solitary solution, periodic solution, rational function solutions and jacobian function solution ), backlund transformation, cole - hopf transformation, dromion solution and its construction etc. charter 2 introduces ac = bd model and its application about partial differential equations

    第二部分以構造性的變換及符號計算特別是（吳代數消元法）為工具，來研究非線性演化方程中的一些問題：精確解（如孤子解、周期解、有理解和雅可比橢圓函數解（雙周期解）等） 、 backlund變換、 hopf變換， dromion解及衰變結構等第二章介紹了求解pdes的ac = bd模式及其在偏微分方程中的作用。
  3. ( 1 ) based on two types of riccati equations, two kinds of new methods are proposed to obtain solutions of nonlinear differential equations. twelve families of exact solutions of wbk equation are found by using one of two methods ; ( 2 ) the homogeneous balance method is improved cind investigated to ( 2 + l ) - dimensional broer - kaup equation such that many families of new solutions are derived. ( 4 ) based on the isospectral lax pair of riccati form for generalized kdv equation with the force term, new darboux transformation and solitary - like wave solutions and rational solutions are obtained ; ( 4 ) by constructing darboux transformation and the superposition formula of generalized variable coefficients kdv equation with the force term, new single solitary - like wave solutions, double solitary - like wave solutions and rational solutions are found for ( 2 + l ) - dimensional generalized kp equation

    第二章和第三章考慮非線性偏微分方程的精確解的構造：首先給出了c - d對和c - d可積系統的基本理論，然後在第三章中具體研究了它們的應用： （ 1 ）基於兩種riccati方程，提出了兩種新的求解非線性微分方程更多解的方法，利用其中的一種方法，得到了wbk方程的12組精確解； （ 2 ）對齊次子衡法進行改進，以致於獲得了（ 2 + 1 ） -維broer - kaup方程的很多新解； （ 3 ）基於帶有外力項的廣義kdv方程的riccati形式的非等譜lax對，提出了該方程的一個新的darboux變換，利用該變換，得到了新的類孤波解和有理解； （ 4 ）通過構造了帶有外力項的變系數kdv方程的darboux變換及疊加原理，獲得（ 2 + 1 ） -維廣義kp方程的新的類單孤波解、雙類孤波解和有理解。
  4. This algorithm is an extension of real root isolation algorithm for univarioie rational polynomial. it results in an higher - dimensional isolated interval for each isolated real root. in the ordinary differential equation qualitative or stability analysis, lienard systems are typical

    Li nard系統是常微分方程定性及穩定性分析研究中一類典型的系統，它不僅在應用領域有著廣泛的運用，在其他微分系統的定性及穩定性分析研究中，也經常會藉助到它豐富的結論。
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