论文标题
使用数值分析延续
Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation
论文作者
论文摘要
木桩链中的行进波通常是纳米翅目，由中央孤立波和指数小的振荡组成。这些振荡已使用指数渐近方法研究，通常需要明确的前阶行为形式。对于许多非线性系统，例如颗粒状木桩链，不可能明确计算前阶溶液。我们表明，可以使用数值近似代替确切的前阶行为来获得准确的渐近近似值。我们计算了Toda木质链条的振荡行为，并将结果与基于Tanh拟合，padé近似体和自适应Antoulas-Andoulas-Anderson（AAA）方法的指数渐近学进行了比较。显示AAA方法可产生最准确的振荡幅度和振荡消失的质量比的预测。然后，将此方法应用于研究颗粒状木桩链，包括具有赫兹相互作用的链 - 该方法能够计算出在先前研究中无法准确近似的行为。
Travelling waves in woodpile chains are typically nanoptera, which are composed of a central solitary wave and exponentially small oscillations. These oscillations have been studied using exponential asymptotic methods, which typically require an explicit form for the leading-order behaviour. For many nonlinear systems, such as granular woodpile chains, it is not possible to calculate the leading-order solution explicitly. We show that accurate asymptotic approximations can be obtained using numerical approximation in place of the exact leading-order behaviour. We calculate the oscillation behaviour for Toda woodpile chains, and compare the results to exponential asymptotics based on tanh-fitting, Padé approximants, and the adaptive Antoulas-Anderson (AAA) method. The AAA method is shown to produce the most accurate predictions of the amplitude of the oscillations and the mass ratios for which the oscillations vanish. This method is then applied to study granular woodpile chains, including chains with Hertzian interactions -- this method is able to calculate behaviour that could not be accurately approximated in previous studies.
