一维非线性双原子链晶格振动的色散关系

在小振动情况下，讨论非简谐项对一维双原子链晶格振动色散关系的影响；对于三次方在位非线性力的作用，得到一维双原子非线性链晶格振动的色散关系，分析了光频支和声频支色散关系在非线性作用下的变化；色散关系的频隙在非线性力的作用下发生变化，且频隙的位置将降低（非线性系数为正）或升高（非线性系数为负）。

The Dispersion Relation of One-Dimensional Nonlinear Diatomic Chain

The linear dispersion relation of a one dimensional diatomic chain will be changed when the nonlinear reactions between the atoms are considered. Nonlinearity is fascinating because it makes many things changed. The dispersion relation of linear atomic chain is well known. It describes the linear oscillations of the chain . When the atoms are subjected to a nonlinear symmetric on site potential, the dispersion relation is studied. The changes of dispersion relation of optical and acoustic wave are discussed. It is called the nonlinearity induced changes. The width and position of the gap are analyzed. The nonlinearity induced gap solitons can be discussed further.