带有超二次位势无限格点上的基态行波解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1451-1461.

带有超二次位势无限格点上的基态行波解

邵春晖¹(),孙吉江^1,*(),马世旺²()

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

收稿日期:2021-03-01 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 孙吉江 E-mail:sch19970606@qq.com;sunjijiang2005@163.com;shiwangm@163.net
作者简介:邵春晖, E-mail: sch19970606@qq.com|马世旺, E-mail: shiwangm@163.net
基金资助:
国家自然科学基金(11861046);江西省自然科学基金(20212BAB201026)

Ground State Travelling Waves in Infinite Lattices with Superquadratic Potentials

Chunhui Shao¹(),Jijiang Sun^1,*(),Shiwang Ma²()

¹ School of Mathematics and Computer Sciences, Nanchang University, Nanchang 330031
² School of Mathematical Sciences, Nankai University, Tianjin 300071

Received:2021-03-01 Online:2022-10-26 Published:2022-09-30
Contact: Jijiang Sun E-mail:sch19970606@qq.com;sunjijiang2005@163.com;shiwangm@163.net
Supported by:
the NSFC(11861046);the Natural Science Foundation of Jiangxi Province(20212BAB201026)

摘要/Abstract

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 $\ddot{q}_n= U'(q_{n+1}-q_n)-U'(q_n-q_{n-1}), \quad n\in{\Bbb 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.

关键词: 格点动力系统, 基态行波解, 周期, 孤立, 超二次

Abstract:

In this paper, we consider one dimensional FPU type lattices with particles of unit mass. The dynamics of the system is described by the following $\ddot{q}_n= U'(q_{n+1}-q_n)-U'(q_n-q_{n-1}), \quad n\in{\mathbb 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.

Key words: Lattice dynamical systems, Ground state travelling waves, Periodic, Solitary, Superquadratic

中图分类号:

O175.7

邵春晖,孙吉江,马世旺. 带有超二次位势无限格点上的基态行波解[J]. 数学物理学报, 2022, 42(5): 1451-1461.

Chunhui Shao,Jijiang Sun,Shiwang Ma. Ground State Travelling Waves in Infinite Lattices with Superquadratic Potentials[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1451-1461.

参考文献 20

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