The Second Order Eigenvalue Problem That A Type Of The Energy Which Dependented On Speed And Its Integerable System

This article first introduces the history and current situation of the development of the theory of soliton.Then by studying the Bargmann system related to the second order eigenvalue problem:This article first determined the Hamilton operator K and J,Step by step, we have to discuss the characteristics of the value of the problem of equation,then Bargmann constraint condition has been determined. Reuse Bargmann constrained quadratic eigenvalue problem can be converted to Bargmann system. According to the theory of mechanical system which Hamilton mechanicsand Euler-Lagrange equation mentioned, Using the density function of Lagrange to establish a set of reasonable coordinates on the symplectic manifold, And using this set of reasonable coordinates,make the Bargmann system which corresponded to the eigenvalue problem into the regular finite Regular system which called Hamilton.under the theory of integrable confocal involutory system and generating function and the meaning of Liouville integrable etc, Hamilton canonical system is obtained.