带有超二次位势无限格点上的基态行波解

Abstract

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

CLC Number:

O175.7

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.

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References 20

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Ground State Travelling Waves in Infinite Lattices with Superquadratic Potentials

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