凸FPU型链中的异宿行波
Heteroclinic travelling waves in convex FPU-type chains
摘要：
我们考虑具有一般凸势的无穷FPU型原子链，研究了连接常数渐近态的异宿行波的单调前沿的存在性。Looss表明，小振幅锋从力的凹凸转折点分叉。在本文中，我们证明了前线存在的任何渐近状态，满足一定的约束。对于其导数恰好有一个转折点的潜力，这些限制恰恰意味着前面对应于能量守恒的超音速激波的“p-系统”，这是天真的双曲连续极限的链。证明是通过最小化偏离这种不连续激波轮廓的作用函数来进行的。我们还讨论了波前的定性性质和数值计算。
英文摘要：
We consider infinite FPU-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 precisely mean 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 goes via minimizing an action functional for the deviation from this discontinuous shock profile. We also discuss qualitative properties and the numerical computation of fronts.
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