数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (3): 782-790.doi: 10.1016/S0252-9602(16)30039-X

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GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES

张鲁豫, 马世旺   

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
  • 收稿日期:2015-03-26 修回日期:2015-11-18 出版日期:2016-06-25 发布日期:2016-06-25
  • 作者简介:Luyu ZHANG,E-mail:zhangluyu2009@163.com;Shiwang MA,E-mail:shiwangm@163.net
  • 基金资助:

    Research supported by the Specialized Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation of China.

GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES

Luyu ZHANG, Shiwang MA   

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
  • Received:2015-03-26 Revised:2015-11-18 Online:2016-06-25 Published:2016-06-25
  • Supported by:

    Research supported by the Specialized Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation of China.

摘要:

In this paper, we consider FPU lattices with particles of unit mass. The dynamics of the system is described by the infinite system of second order differential equations
qn=U'(qn+1-qn)-U'(qn-qn-1), n∈Z,
where qn denotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles. Inspired by previous work due to Szulkin and Weth (Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 (2009), 3802-3822), we investigate the existence of solitary ground waves, i.e., nontrivial solutions with least possible energy.

关键词: FPU lattice, ground state wave, Nehari manifold

Abstract:

In this paper, we consider FPU lattices with particles of unit mass. The dynamics of the system is described by the infinite system of second order differential equations
qn=U'(qn+1-qn)-U'(qn-qn-1), n∈Z,
where qn denotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles. Inspired by previous work due to Szulkin and Weth (Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 (2009), 3802-3822), we investigate the existence of solitary ground waves, i.e., nontrivial solutions with least possible energy.

Key words: FPU lattice, ground state wave, Nehari manifold

中图分类号: 

  • 37K60