带有超二次位势无限格点上的基态行波解  

Ground State Travelling Waves in Infinite Lattices with Superquadratic Potentials

作　　者：邵春晖 孙吉江 马世旺[2] Chunhui Shao;Jijiang Sun;Shiwang Ma(School of Mathematics and Computer Sciences,Nanchang University,Nanchang 330031;School of Mathematical Sciences,Nankai University,Tianjin 300071)

机构地区：[1]南昌大学数学与计算机学院,南昌330031 [2]南开大学数学科学学院,天津300071

出　　处：《数学物理学报（A辑）》2022年第5期1451-1461,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11861046);江西省自然科学基金(20212BAB201026)。

摘　　要：该文考察了一维格点上均为单位质量粒子的FPU型格点问题.这个系统的动力学方程描述如下q_(n)=U′(q_(n)+1−q_(n))−U′(q_(n)−q_(n)−1),n∈Z,其中U是相邻两个粒子相互作用产生的位势,q_(n)(t)是第n个粒子在时刻t的状态.通过直接使用通常的变分方法,比起Pankov[10],Zhang和Ma^([20])之前的工作,该文在更加宽泛的条件下研究了这类系统的基态行波解(即具有最小能量的非平凡行波解)的存在性.并且文中还讨论了孤立基态行波的单调性.In this paper,we consider one dimensional FPU type lattices with particles of unit mass.The dynamics of the system is described by the followingq_(n)=U′(q_(n)+1−q_(n))−U′(q_(n)−q_(n)−1),n∈Z,where U is the potential of interaction between two adjacent particles and q_(n)denotes the displacement.By directly using the usual variational method,we study the existence of ground state travelling waves,i.e.,non-trivial travelling waves with least possible energy,for the above system with more general superquadratic potentials than the previous work of Pankov[10]and Zhang and Ma^([20]).Moreover,we also concern the monotonicity of the solitary ground state travelling waves.

关 键 词：格点动力系统 基态行波解 周期 孤立 超二次 

分 类 号：O175.7[理学—数学]