GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES

doi:10.1016/S0252-9602(16)30039-X

Acta mathematica scientia,Series B ›› 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

Luyu ZHANG, Shiwang MA

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.

Abstract

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
q_n=U'(q_n+1-q_n)-U'(q_n-q_n-1), n∈Z,
where q_n 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

CLC Number:

37K60

Luyu ZHANG, Shiwang MA. GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES[J].Acta mathematica scientia,Series B, 2016, 36(3): 782-790.

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GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES

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