Preprints
- Stability of asymptotic waves in the Fisher-Stefan equation.
Submitted. 16 pages.
With T.T.H. Bui and P. van Heijster (2024).
ArXiv link
(pdf)
- Floquet theory and stability analysis for Hamiltonian PDEs.
Submitted. 37 pages.
With J.C. Bronski, and V. M. Hur (2023).
ArXiv link
(pdf)
Publications
- A geometric singular perturbation analysis of generalised shock selection rules in reaction-nonlinear diffusion models.
SIAM Journal of Applied Dynamical Systems (SIADS) 23 (3) DOI:10.1137/23M1591803
With B. H. Bradshaw-Hajek, I. Lizarraga, and M. Wechselberger (2023).
ArXiv link
(pdf)
- Analytic shock-fronted solutions to a reaction-diffusion equation with negative diffusivity.
To appear in Studies in Applied Mathematics. 35 pages.
With B. H. Bradshaw-Hajek, T. Miller, A. K. Y. Tam, and M. Wechselberger (2024).
ArXiv link
(pdf)
- Nonlinear stability of shock-fronted travelling waves under nonlocal regularization.
To Appear in Physica D: Nonlinear Phenomena. 460 DOI:
10.1016/j.physd.2024.134069.
With I. Lizarraga (2024).
ArXiv link
(pdf)
- An Evans function for the linearised 2D Euler equations using Hill's determinant.
Physica D: Nonlinear Phenomena 457 DOI: 10.1016/j.physd.2023.133954.
With H. R. Dullin (2024).
ArXiv link
(pdf)
- Hamiltonian spectral flows, the Maslov index, and the stability of standing waves in the nonlinear Schrödinger equation.
SIAM Journal on Mathematical Analysis (SIMA). 55 (5). DOI: 10.1137/22M1533797
With M. Curran, G. Cox, and Y. Latushkin (2023).
ArXiv link
(pdf)
- Spectral stability of shock-fronted travelling waves under viscous relaxation.
J. Nonlinear Sci 33 82 DOI: 10.1007/s00332-023-09941-x
With I. Lizarraga (2023).
ArXiv link
(pdf)
- A geometric singular perturbation analysis of regularised reaction-nonlinear diffusion models including shocks.
Proceedings of the 47th Sapporo Symposium on Partial Differential Equations.
DOI:10.14943/103871 pp. 53-64
With B. Bradshaw-Hajek, I. Lizarraga, and M. Wechselberger (2022).
(pdf)
- Rigorous justification of the Whitham modulation equations for equations of Whitham-type.
Studies in Applied Mathematics. 149 (2) pp. 297-323. DOI: 10.1111/sapm.12500
With W. A. Clarke and W. Perkins (2022).
ArXiv link
(pdf)
- Classification and stability analysis of polarising and depolarising travelling wave solutions for a model of collective cell migration.
Applied Mathematics and Computation. 421. DOI:10.1016/j.amc.2022.126954
With N. Rahman and D. Oelz (2022).
ArXiv link
(pdf)
- Generalized Maslov Indices for non-Hamiltonian systems.
SIAM Journal on Mathematical Analysis (SIMA). 54 (2) DOI:10.1137/20M1381319.
With T.J. Baird, P. Cornwell, G. Cox, and C.K.R.T. Jones (2022).
ArXiv link
(pdf)
- Rigorous justification of the Whitham modulation theory for equations of NLS type.
Studies in Applied Mathematics. 147 (2) pp. 577--621.
DOI:10.1111/sapm.12390
With W. A. Clarke (2021).
ArXiv link
(pdf)
- Stability of traveling wave solutions of nonlinear dispersive equations of NLS type. Archive of Rational Mechanics and Analysis. 240 pp.927-969
With K. P. Leisman, J. C. Bronski, and M. A. Johnson (2021).
ArXiv link
(pdf)
- Traveling wave solutions in a model for tumor invasion with the acid-mediation hypothesis. Journal of Dynamics and Differential Equations. 88 DOI:10.1007/s10884-021-10003-7
With P.N. Davis, P van Heijster and M.R. Rodrigo (2021).
ArXiv link
(pdf)
- Standing waves on a flower graph.
Journal of Differential Equations. 271 pp. 719--763 DOI:10.1016/j.jde.2020.09.010
With A. Kairzhan, D. Pelinovsky, and K.L. Xiao (2021).
ArXiv link
(pdf)
- A new Evans function for quasi-periodic solutions of the linearised sine-Gordon equation.
Journal of Nonlinear Science. 30 (6) pp 3421--3442 DOI:10.1007/s00332-020-09655-4
With W. A. Clarke (2020).
ArXiv link
(pdf)
- Slow unfoldings of contact singularities in singularly perturbed systems beyond the standard form.
Journal of Nonlinear Science. 30 (6) pp. 3161-3198. DOI:10.1007/s00332-020-09647-4
With I. Lizarraga, and M. Wechselberger (2020).
ArXiv link
(pdf)
- Travelling wave solutions in a negative nonlinear diffusion-reaction model. Journal of Math Biology 81 (6) pp. 1495--1522. DOI:10.1007/s00285-020-01547-1
With Y. Li, P. van Heijster, and M. J. Simpson (2020).
ArXiv link
(pdf)
- Symmetry breaking bifurcations in the NLS equation with an asymmetric delta potential.
Nonlinear Dynamics. 100 (4) pp. 3815--3824. DOI: 10.1007/s11071-020-05730-3
With R. Rusin, and H. Susanto (2020).
ArXiv link
(pdf)
- (In)stability of travelling waves in a model of haptotaxis. SIAM Journal on Applied Mathematics. 80 (4) pp. 1629-1653. DOI: 10.1137/19M1259705
With K.E. Harley, P. van Heijster, G. J. Pettet, T.V. Roberts, and M. Wechselberger (2020).
ArXiv link
(pdf)
- Instability of unidirectional flows for the 2D α-Euler equations.Comm. Pure. Appl. Analysis. 19 (4) pp. 2051--2079.
With H. Dullin, Y. Latushkin, S. Vasudevan and J. Worthington (2020).
ArXiv link
(pdf)
- Spectral stability of travelling wave solutions in a Keller-Segel model. Applied Numerical Mathematics. 141 pp. 54--61.
With P.N. Davis and P van Heijster (2019).
ArXiv link
(pdf)
- Stability of travelling waves in a Wolbachia invasion. Discrete and Continuous
Dynamical Systems - Series B 23 (2) pp. 609-628. With M. H. Chan and P. S. Kim (2018).
ArXiv link
(pdf)
- Absolute instabilities of travelling wave solutions in a Keller-Segel model. Nonlinearity. 30 (11) pp 4029-4061. With P.N. Davis and P van Heijster (2017).
ArXiv link
(pdf)
Selected for Nonlinearity's 2017 Highlights Collection.
- Instability of equilibria for the 2D Euler equations on the torus. SIAM Journal of Applied Mathematics. 76 (4) pp. 1446-1470. With H. R. Dullin and J. Worthington. (2016).
ArXiv link (pdf)
- On the spectral and modulational stability of periodic wavetranes for nonlinear Klein-Gordon equations. Bulletin of the Brazilian Mathematical Society. 47 (2) pp. 471-429. With C.K.R.T. Jones, P. D. Miller, and R. G. Plaza. (2016).
- Dynamical Hamiltonian-Hopf instabilities of periodic traveling waves in Klein-Gordon equations. Physica D: Nonlinear Phenomena.
308 pp 87-93. With P.D. Miller (2015).
ArXiv link (pdf)
- Numerical computation of an Evans function for travelling waves. Mathematical Biosciences. 266 pp 36-51. With K. Harley, P. v Heijster, G.J. Pettet and M. Wechselberger. (2015).
ArXiv link (pdf)
- Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon Equation. Journal of Differential Equations. 257 pp.4632-4703. DOI 10.1016/j.jde.2014.09.004 With C.K.R.T. Jones, P.D. Miller and R. G. Plaza. (2014). ArXiv Link (pdf)
- Novel solutions for a model of wound healing angiogenesis. Nonlinearity. 27 pp. 2975-3003. With K. Harley, P. v.Heijster, G.J. Pettet and M. Wechselberger. (2014). Link.
ArXiv link (pdf)
- An instability Criterion for Nonlinear Standing Waves on Nonzero Backgrounds. J Nonlinear Science. 24 (6) pp. 1177-1196. DOI 10.1007/s00332-01409215-8. With R.K. Jackson and H. Susanto. (2014). Link. ArXiv Link (pdf)
- Existence of travelling wave solutions for a model of tumour invasion. SIAM Journal of Applied Dynamical Systems (SIADS) 13 (1) pp. 366-396. With K. Harley, P. v.Heijster, G.J. Pettet and M. Wechselberger. (2014).
(pdf)
- The Morse and Maslov indices
for matrix Hill's equations. Proceedings in Symposia in Pure Mathematics. "Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday." 87 pp. 205-234. With C.K.R.T. Jones and
Y. Latushkin. (2013). ArXiv Link (pdf)
- On the stability analysis of periodic sine-Gordon traveling waves. Physica D: Nonlinear Phenomena. 251 pp. 63-74. With C.K.R.T. Jones, P. D. Miller, and R. G. Plaza. (2013).
ArXiv Link (pdf)
- Unstable Gap solitons in
inhomogeneous nonlinear Schrödinger equations. Journal of
Differential Equations 253 (4) pp. 1191-1205. With C.K.R.T. Jones and H. Susanto. (2012). ArXiv Link (pdf)
- The spectrum of travelling
wave solutions to the sine-Gordon equation. Discrete and Continuous
Dynamical Systems - Series S. 5 (12) pp. 925-937.
With C.K.R.T. Jones. (2012). ArXiv Link (pdf)
- Localized standing waves in
inhomogeneous Schrödinger equations. Nonlinearity 23 (5) pp. 2059-2080. With C.K.R.T. Jones and H. Susanto. (2010). ArXiv Link (pdf)
- The general quadruple point
formula. The American Journal of Mathematics 132 (4) pp. 867-896. With R.
Rimányi. (2010). ArXiv Link (pdf)