Heteroclinic Travelling Waves in Convex FPU-Type Chains
Heteroclinic Travelling Waves in Convex FPU-Type Chains
复制标题
凸 FPU 型链中的异斜行波
DOI：
10.1137/080743147
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
J. Rademacher
中科院分区：
文献类型：
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作者：
M. Herrmann;J. Rademacher
我们考虑无限的具有一般凸势的fermi - pasta - ulam型原子链，并研究了连接常渐近态的异斜行波单调前沿的存在性。结果表明，小振幅锋面从力的凹凸拐点分叉。在本文中，我们证明了对于满足一定约束的任何渐近状态，前沿都存在。对于导数只有一个转折点的势，这些约束精确地意味着前缘对应于“p系统”的能量守恒超音速激波，这是链的朴素双曲连续极限。这个证明是通过最小化一个动作函数来实现的，这个动作函数偏离了这个不连续的冲击剖面。我们还讨论了锋面的定性性质和数值计算。
We consider infinite Fermi–Pasta–Ulam-type atomic chains with general convex potentials and study the existence of monotone fronts that are heteroclinic travelling waves connecting constant asymptotic states. Iooss showed that small amplitude fronts bifurcate from convex-concave turning points of the force. In this paper, we prove that fronts exist for any asymptotic states that satisfy certain constraints. For potentials whose derivative has exactly one turning point, these constraints mean precisely that the front corresponds to an energy conserving supersonic shock of the “p-system," which is the naive hyperbolic continuum limit of the chain. The proof is achieved via minimizing an action functional for the deviation from this discontinuous shock profile. We also discuss qualitative properties and the numerical computation of fronts.