二阶非线性扰动差分方程的振动准则

将Gronwall不等式离散化,利用该不等式讨论了二阶非线性扰动差分程的振动性,把Winter和Lighton所建立的关于微分方程的振动性结果推广到差分方程上.

关于扰动差分方程零解的稳定性

讨论了一类扰动差分方程组零解的稳定性 ,一致稳定性 。

关于扰动Volterra型差分方程的两度量稳定性(英文)

讨论了一类扰动Volterra型差分方程,给出了关于扰动系统和非扰动系统的比较原理,并运用这一比较原理和Lyapunov函数方法,给出了扰动Volterra型差分方程的两度量稳定性的判别准则.

Breather Dynamics of the Sine-Gordon Equation

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.