On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term

不可积 Henon-Heiles 系统的多辛结构

Multisymplectic structure of nonintegrable Henon-Heiles system

本文为不可积 Henon-Heiles 系统、Kepler 问题及 Toda 型系统构造第二不变辛形式，并提出可同时保持两种辛形式的多辛积分器。

The Painleve Analysis and Special Solutions for Nonintegrable Systems

The Hénon--Heiles system in the general form is studied. In a nonintegrable case new solutions have been found as formal Laurent series, depending on three parameters. One of parameters determines a location of the singularity point, other parameters determine coefficients of the Laurent series. For some values of these two parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions.

Construction of solutions for the generalized Henon-Heiles system with the help of the Painleve test

The Henon-Heiles system in the general form has been considered. In a nonintegrable case with the help of the Painleve test new solutions have been found as formal Laurent or Puiseux series, depending on three parameters. One of parameters determines a location of the singularity point, other parameters determine coefficients of series. It has been proved, that if absolute values of these two parameters are less or equal to unit, then obtained series converge in some ring. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known exact soluti…

Construction of Special Solutions for Nonintegrable Dynamical Systems with the help of the Painleve Analysis

The generalized Henon-Heiles system has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as Laurent series, depending on three parameters. The obtained series converge in some ring. One of parameters determines the singularity point location, other parameters determine coefficients of series. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions. The Painleve test can be used not only to construct local solutions as the Laurent series but also to find elli…

Construction of Special Solutions for Nonintegrable Systems

The Painleve test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized Henon-Heiles system that the use of the Laurent series solutions of the initial differential equation assists to…