# Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation

@inproceedings{Deng2022ExponentialAO, title={Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation}, author={Guo Deng and Christopher J. Lustri}, year={2022} }

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…

## Figures and Tables from this paper

## References

SHOWING 1-10 OF 86 REFERENCES

### The AAA Algorithm for Rational Approximation

- Computer ScienceSIAM J. Sci. Comput.
- 2018

We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of MATLAB and requiring no user input parameters. Even on a disk o...

### Nanoptera in nonlinear woodpile chains with zero precompression

- MathematicsPhysica D: Nonlinear Phenomena
- 2021

### Solitary wave dynamics in generalized Hertz chains: an improved solution of the equation of motion.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

An iteratively exact solution to describe the solitary wave as a function of material parameters and a universal, infinite set of coefficients, which depend only on n is presented.

### Realization-independent H2-approximation

- 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pages 4953–4958
- 2012

### Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains

- SIAM Journal on Applied Dynamical Systems
- 2021

### Nanoptera and Stokes curves in the 2-periodic Fermi–Pasta–Ulam–Tsingou equation

- MathematicsPhysica D: Nonlinear Phenomena
- 2020

### Nanoptera in a Period-2 Toda Chain

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2018

This work isolates the exponentially small, constant-amplitude waves, `nanoptera', and elucidate the dynamics of these waves in terms of the Stokes phenomenon, finding a simple asymptotic expression for the waves.

### On the generation and propagation of solitary waves in integrable and nonintegrable nonlinear lattices

- Physics
- 2020

We investigate the generation and propagation of solitary waves in the context of the Hertz chain and Toda lattice, with the aim to highlight the similarities, as well as differences between these…

### Exponential node clustering at singularities for rational approximation, quadrature, and PDEs

- Mathematics, Computer ScienceNumerische Mathematik
- 2021

A theoretical model of the tapering effect is proposed based on the Hermite contour integral and potential theory, which suggests that tapering doubles the rate of convergence in rational approximations of functions with singularities.

### Interactions of solitary waves in integrable and nonintegrable lattices.

- PhysicsChaos
- 2020

We study how the dynamics of solitary wave (SW) interactions in integrable systems is different from that in nonintegrable systems in the context of crossing of two identical SWs in the (integrable)…