30 citations · 97 across the 20 of their papers we have counts for
22 papers
The emergence of rapid oscillations in a fifth-order KdV equation
Christopher J. Lustri, S. Jonathan Chapman, Richard C. P. Nicotra
We consider the emergence of rapidly propagating, exponentially small-amplitude oscillations in the impulsively started fifth-order Korteweg--de Vries equation (KdV5), and demonstr…
Appearance of the higher-order Stokes phenomenon in a discrete Airy equation
Aaron J. Moston-Duggan, Christopher J. Howls, Christopher J. Lustri
We study a discrete variant of the Airy equation, formulated as an advance-delay equation, to reveal that discretization induces the higher-order Stokes phenomenon, which is not pr…
Small-time asymptotics and the emergence of complex singularities for the KdV equation
Scott W. McCue, Christopher J. Lustri, Daniel J. VandenHeuvel +3
While real-valued solutions of the Korteweg--de Vries (KdV) equation have been studied extensively over the past 50 years, much less attention has been devoted to solution behaviou…
Borel-Padé exponential asymptotics for the discrete nonlinear Schrödinger model with next-to-nearest neighbour interactions
Christopher J. Lustri, Inês Aniceto, Panayotis G. Kevrekidis
In the present work we study discrete nonlinear Schr{ö}dinger models combining nearest (NN) and next-nearest (NNN) neighbor interactions, motivated by experiments in waveguide arra…
Stokes' phenomenon in continuous limits of discrete Painlevé I
Christopher J. Lustri, John R. King
We use exponential asymptotic analysis to identify the relevance of Stokes' phenomenon to integrability in discrete systems. We study Stokes' phenomenon in two discrete problems wi…
On the selection of Saffman-Taylor viscous fingers for divergent flow in a wedge
Cecile Andersen, Christopher J. Lustri, Scott W. McCue +1
We study self-similar viscous fingering for the case of divergent flow within a wedge-shaped Hele-Shaw cell. Previous authors have conjectured the existence of a countably-infinite…
Exponential Asymptotics using Numerical Rational Approximation in Linear Differential Equations
Christopher J. Lustri, Samuel C. Crew, S. Jonathan Chapman
Singularly-perturbed ordinary differential equations often exhibit Stokes' phenomenon, which describes the appearance and disappearance of oscillating exponentially small terms acr…
Locating complex singularities of Burgers' equation using exponential asymptotics and transseries
Christopher J. Lustri, Ines Aniceto, Daniel J. VandenHeuvel +1
Burgers' equation is an important mathematical model used to study gas dynamics and traffic flow, among many other applications. Previous analysis of solutions to Burgers' equation…
Burgers' equation in the complex plane
Daniel J. VandenHeuvel, Christopher J. Lustri, John R. King +2
Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following o…
Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation
Guo Deng, Christopher J. Lustri
Travelling waves in woodpile chains are typically nanoptera, which are composed of a central solitary wave and exponentially small oscillations. These oscillations have been studie…
Exponential asymptotics for elastic and elastic-gravity waves on flow past submerged obstacles
Christopher J. Lustri
Linearized flow past a submerged obstacle with an elastic sheet resting on the flow surface are studied in the limit that the bending length is small compared to the obstacle depth…
Nanoptera In Higher-Order Nonlinear Schrödinger Equations: Effects Of Discretization
Aaron J. Moston-Duggan, Mason A. Porter, Christopher J. Lustri
We consider generalizations of nonlinear Schrödinger equations, which we call "Karpman equations", that include additional linear higher-order derivatives. Singularly-perturbed Kar…
Nanoptera in nonlinear woodpile chains with zero precompression
Guo Deng, Christopher J. Lustri
We use exponential asymptotics to study travelling waves in woodpile systems modelled as singularly perturbed granular chains with zero precompression and small mass ratio. These s…
Nanoptera in weakly nonlinear woodpile and diatomic granular chains
Guo Deng, Christopher J. Lustri, Mason A. Porter
We study ``nanoptera'', which are non-localized solitary waves with exponentially small but non-decaying oscillations, in two singularly-perturbed Hertzian chains with precompressi…
Capturing the cascade: a transseries approach to delayed bifurcations
Inês Aniceto, Daniel Hasenbichler, Christopher J. Howls +1
Transseries expansions build upon ordinary power series methods by including additional basis elements such as exponentials and logarithms. Alternative summation methods can then b…
Kelvin wake pattern at small Froude numbers
Ravindra Pethiyagoda, Timothy J. Moroney, Christopher J. Lustri +1
The surface gravity wave pattern that forms behind a steadily moving disturbance is well known to comprise divergent waves and transverse waves, contained within a distinctive V-sh…
Nanoptera and Stokes Curves in the 2-Periodic Fermi-Pasta-Ulam-Tsingou Equation
Christopher J. Lustri
This work presents asymptotic solutions to a singularly-perturbed, period-2 FPUT lattice and uses exponential asymptotics to examine `nanoptera', which are nonlocal solitary waves…
On Asymptotics of Optimal Stopping Times
Hugh Entwistle, Christopher Lustri, Georgy Sofronov
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a pro…
Selection of a Hele-Shaw bubble via exponential asymptotics
Christopher J. Lustri, Christopher C. Green, Scott W. McCue
The well-studied selection problems involving Saffman-Taylor fingers or Taylor-Saffman bubbles in a Hele-Shaw channel are prototype examples of pattern selection. Exact solutions t…
Three-dimensional capillary waves due to a submerged source with small surface tension
Christopher J. Lustri, Ravindra Pethiyagoda, S. Jonathan Chapman
Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary wave…
The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell
Christopher C Green, Christopher J Lustri, Scott W McCue
New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conform…
Nanoptera in a Period-2 Toda Chain
Christopher J. Lustri, Mason A. Porter
We study asymptotic solutions to a singularly-perturbed, period-2 Toda lattice and use exponential asymptotics to examine `nanoptera', which are nonlocal solitary waves with consta…