The Canonical Formalized Structure Question Of Infinite-dimensional Hamiltonian Systems And Its Applications

The Hamilton system is a special kind of partial differential equations(groups).It has good symmetry and universality.It plays an important role in the research of many disciplines and is a powerful tool.Therefore,the research is carried out under the Hamilton system.It has great practical significance.Among them,the problem of Hamilton formalization is a very important problem.At present,there are many methods to transform into Hamilton canonical form.Continue to develop these methods is what we are pursuing,especially to get a faster and more intuitive method can make the use of these methods wider.This article mainly studies the structural problem of the infinite-dimensional Hamilton regular formalization.The first chapter started with the main line the infinite-dimensional Hamilton canonical system.First,the research object of this article was introduced,and the related definitions of the Hamilton canonical form studied in this article were introduced.Secondly,The development history and research methods of some infinite-dimensional Hamilton canonical formalizations were listed.Finally,the research ideas and main results obtained in this article were explained.The second chapter mainly discussed the structural characteristics of the Hamilton operator of high-order partial differential equations.Firstly,on the basis of the predecessors,the Hamilton operator was rewritten into a general summation form.Then,the condition that the characteristic polynomial is zero,The idea of limiting coefficients and parameters was adopted to solve the equations from the bottom-up.Finally,not only the natural limiting relationship satisfied by the parameters was obtained,but also the prerequisite guarantee for the solution of the differential equation was provided.The solutions of two types of special Hamilton operators were determined,and the feasibility and convenience of the conclusions were verified through several examples.The third chapter mainly studies the structural characteristics of the Hamiltonian operator of low-order partial differential equations.First,the top-down reduction of the equation system determined by the coefficient matrix is solved,and not only the infinite-dimensional Hamiltonian of the second-order differential equation is obtained.and under appropriate conditions,the solutions of five special Hamilton operators are obtained;then according to the solution of the operator to find the corresponding examples,and made a summary.The last chapter summarizes the work of the full text and points out the shortcomings of this article.And the work that may continue in the future.