hamilton-jacobi equations 中文意思是什麼
hamilton-jacobi equations
解釋
哈密爾頓-雅戈比方程-
In this article, we give sufficient conditions for the existence of solutions to the vectorial hamilton - jacobi equations with dirichlet boundary condition : obtaining, in addition, an application to the theory of existence of minimizers for a class of non - convex variational problems
本文給出了一類依賴于自變量和未知函數的梯度的向量情況隱式偏微分方程的dirichlet問題的弱解的存在性的充分條件，並將該結果應用到一類非擬凸變分問題中去。 -
From maxwell equations the refractive index equation and hamilton - jacobi equation, which describe the evolution of the electric field, are derived including the effects of the diffraction, the third - order intensity - dependent nonlinearity, plasma defocusing, the focusing and defocusing of the plasma channel, and the relativistic self - focusing
從maxwell方程出發我們得到了兩個包含衍射、三階強度非線性、等離子體散焦、等離子體隧道聚焦和散焦以及相對論自聚焦等效應在內的激光場演化方程，即折射率方程和哈密頓-雅可比方程。 -
In this paper, we convert the complex third order eigenvalue problems into the real third order eigenvalue problems. then, based on the euler - lagrange equation and legendre transformation, a reasonable jacobi - ostrogredsky coordinate system have been found, then using nonlinear method, the lax pairs of the real bargrnann and neumann system are nonlinearized, so as to be a new finite - dimensional integrable hamilton system in the liouville sense is generated. moreover, the involutive representations of the solution for the evolution equations are obtained
本文將復的三階特徵值問題轉化為實的三階特徵值問題，利用euler - lagrange方程和legendre變換，找到一組合理的實的jacobi - ostrogredsky坐標系，從而找到與之相關的實化系統，再利用曹策問教授的非線性化方法，分別將三階特徵值問題及相應的lax對進行非線性化，從而得到bargmann勢和neumann勢約束系統，並證明它們是liouville意義下的完全可積系統，進而給出了bargmann系統和neumann系統的對合解。
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