准一维单原子晶格非线性振动方程的双周期解

The Douball-Periodical Solutions of Nonlinear Vibration Equation in Quasi-one-dimensional Monoatomic Lattice

利用行波变量代换和辅助椭圆方程法,求解了准一维单原子非线性晶格振动方程,得到了新的双周期波形式的椭圆函数解.在极限情形下,不仅可以还原为前人给出的扭结孤子解,同时还给出了一类新的类孤子解.

The equations of nonlinear vibration in quasi-one-dimensional monoatomic lat- tice were solved by virtue of the method of travelling wave transformation and auxiliary elliptic equation. Some new double-periodical solutions in terms of Jaccobi elliptic func- tions are obtained. When the module of Jaccobi elliptic function tends to zero, these new double-periodical solutions degenerate the kink-solitons and like-solitons of nonlinear vibra- tion equation in quasi-one-dimensional monoatomic lattice.