Preprints

• Detecting eigenvalues in a fourth-order NLS equation with a non-regular Maslov Box. Submitted. 47 pages. With M. Curran (2024). ArXiv link (pdf)
  


• Shock selection in reactiondiffusion equations with partially negative diffusivity using nonlinear regularisation Submitted. 31 pages. With B. H. Bradshaw-Hajek, T. Miller, A. K. Y. Tam, and M. Wechselberger (2024). ArXiv link (pdf)
  

Publications

1. Stability of asymptotic waves in the Fisher-Stefan equation. Physica D : Nonlinear phenomena. 470 (A) 134383 DOI:10.1016/j.physd.2024.134383 With T.T.H. Bui and P. van Heijster (2024). ArXiv link (pdf)
   


2. Floquet theory and stability analysis for Hamiltonian PDEs. Nonlinearity. 37 (12) 125010 DOI: 10.1088/1361-6544/ad8698 With J.C. Bronski, and V. M. Hur (2024). ArXiv link (pdf)
   


3. 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)
   


4. 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)
   


5. 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)
   
   
6. 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)
   


7. 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)
   


8. 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)
   


9. 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)
   


10. 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)
    


11. 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)
    


12. 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)
    


13. 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)
    


14. 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)
    
    
15. 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)
    


16. 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)
    


17. 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)
    


18. 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)
    
    
19. 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)
    


20. 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)
    


21. (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)
    


22. 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)
    


23. 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)
    


24. 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)
    


25. 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.


26. 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)
    


27. 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).
    


28. 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)
    


29. 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)
    


30. 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)
    


31. 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)
    


32. 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)
    


33. 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)
    


34. 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)
    


35. 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)
    


36. 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)
    


37. 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)
    


38. 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)
    


39. The general quadruple point formula. The American Journal of Mathematics 132 (4) pp. 867-896. With R. Rimányi. (2010). ArXiv Link (pdf)