用G'/G-展开法求解相对论Toda格子方程

摘要

The relativistic Toda lattice equation is used to describe particle vibrations in lattices with an exponential interaction force. Based on the homogeneous balance principle, the G'/G-expansion method is applied to the two type of relativistic Toda lattice equations. We obtain the hyperbolic function solitary wave solutions, the trigonometric function periodic wave solutions and the rational wave solutions with more arbitrary parameters. The exact solutions are useful to research the physical mechanism of the phenomena described by the relativistic Toda lattice equations.%相对论Toda格子方程描述了格子中在指数形式相互作用力作用下的粒子运动.本文依据齐次平衡原则,利用G'/G-展开法求解出两种形式相对论Toda格子方程组的双曲函数形式孤波解、三角函数形式周期波解和有理函数形式行波解,这些精确解含有较多的任意参数；得到的精确解对格子中在指数形式相互作用力作用下粒子运动的研究具有重要理论价值.