| 1. | Transversal heteroclinic orbits for a perturbed sine - gordon equation
方程的横截异宿轨 |
| 2. | An analytical expression of homoclinic orbit or heteroclinic orbit is worked out
得出了同宿轨道或异宿轨道的解析表达式。 |
| 3. | On heteroclinic orbit and progressive wave solution of a class of nonlinear partial differential equations
的降低和共存区域范围变小的结论;证实了在一定的总能范围内类固 |
| 4. | By using melnikov method , the melnikov function of homoclinic orbit or heteroclinic orbit is calculated and established
应用melnikov方法，计算并建立了同宿轨道或异宿轨道的melnikov函数。 |
| 5. | Within the homoclinic orbit or heteroclinic orbit , the analytical expression of one set of periodical track surrounding the center - type singular point is worked out
得到了同宿轨道或异宿轨道内的，围绕中心型奇点的一族周期轨道的解析表达式。 |
| 6. | The quadratic nonlinear term and the cubic nonlinear term that coexist in equation ( 1 ) , thus causes difficulty in studying this sort of system through the analytical method and correspondingly makes the solution of analytical expression of homoclinic orbit or heteroclinic orbit in hamilton system extremely difficult
二次非线性项和三次非线性项共同存在于方程( 1 )中，使得用解析方法研究这类系统的难度增大，对应hamilton系统中的同宿轨道或异宿轨道的解析表达式的求解相当困难。 |
| 7. | This paper is concerned with , the existence and stability of travelling wave solutions for the viscous balance law which is an extension of viscous conservation law where a reaction term g ( u ) is added . l ) the existence of travelling wave solutions by geometric singular perturbation method , we investigate the existence of travelling waves ( a2 ) connecting a saddle point and a sink point and the existence of viscous shock waves c connecting two adjacent or disadjacent saddle points . by giving a detailed analysis of the fast and slow manifolds and verifying the transversality of the intersection of singular stable and unstable manifolds of the reduced problem along the singular heteroclinic orbit , we obtain the existence of travelling waves ( a2 ) in the case of a convex flow function / and that of viscous shock waves c under the assumption that f " is bounded
主要结果如下： 1 )行波的存在性本文利用[ 37 ]中几何奇异摄动理论，通过仔细分析= 0时的快流、慢流，验证= 0时慢流方程的稳定与不稳定流形横截相交于奇异异宿轨道，先在f为凸的条件下严格证明了( )存在连接不相邻的鞍点、结点的行波( a2 ) ；然后在地f有界的条件下得到( )存在连接鞍点(包括相邻和不相邻)的粘性冲击波c ，弥补了[ 11 ]缺少严格证明的不足，并推广了[ 11 ]在f为凸的条件下得到的粘性冲击波的存在性结果。 |
| 8. | Every result in the paper is presented through specific analytic expression , including the analytic expression of homoclinic orbit or heteroclinic orbit and its melnikov function , analytical expression of periodical track surrounding the center - type singular point within the homoclinic orbit or heteroclinic orbit and its melinkov function , the critical value when periodical m point appears , the critical value when smale horseshoes chaos appears , etc .
文中的各个结果均以具体的解析形式给出，其中包括同宿轨道或异宿轨道的解析表达式及其melnikov函数；同(异)宿轨道内围绕中心型奇点的周期轨道的解析表达式及其melnikov函数；出现周期m点的临界值；出现smale马蹄混沌的临界值等。 |
| 9. | Nature of the singular point of plane poincare mapping that is established by equation ( 1 ) is analyzed . relationship between the three parameters and homoclinic orbit and heteroclinic orbit of the hamilton system corresponding to this sort of equation is discussed . the adequate and essential condition of the existing homoclinic orbit or heteroclinic orbit for the hamilton system is presented
分析了方程( 1 )建立的平面poincare映射的奇点性质，讨论了此类方程对应的hamilton系统的同宿轨道和异宿轨道与三个参数o 、夕、尸的关系，给出了hamilton系统存在同宿轨道或异宿轨道的充分必要条件。 |
| 10. | All of these reveal the further properties of the wave propagating in one - dimensional elastic continuum . on phase plane , the qualitative analysis are made , which exhibits four kinds of orbits : the heteroclinic orbit of burgers equation , the homoclinic orbit of k - dv equation , and saddle - foci heteroclinic orbit or saddle - joint heteroclinic orbit of kdv - burgers equation
说明burgers方程在相平面上有相应于激波解的异宿轨道; k ~ dv方程有相应于孤波解的同宿轨道: kdv一buegers方程有相应于振荡孤波解的鞍一焦异宿轨道和相应于激波解的鞍一结异宿轨道。 |
