Preprints

• P Carter, A Doelman, P van Heijster, D Levy, P Maini, E Okey, P Yeung.
  Deformations of acid-mediated invasive tumors in a model with Allee effect. (pdf)
• M Avery, P Carter, B de Rijk, A Scheel.
  Stability of coherent pattern formation through invasion in the FitzHugh-Nagumo system. (pdf)
• S Banerjee, M Baudena, P Carter, R Bastiaansen, A Doelman, and M Rietkerk.
  Rethinking tipping points in spatial ecosystems.

Research articles

• P Carter, A Doelman, A Iuorio, F Veerman.
  Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model.
  Nonlinearity 37(9) (2024), 095008. (preprint, arXiv)
• P Carter
  A stabilizing effect of advection on planar interfaces in singularly perturbed reaction-diffusion equations.
  SIAM Journal on Applied Mathematics 84(3) (2024), pp. 1227-1253. (preprint, arXiv)
• T Chin, J Ruth, C Sanford, R Santorella, P Carter, and B Sandstede.
  Enabling equation-free modeling via diffusion maps.
  Journal of Dynamics and Differential Equations 36 (2024), pp. 415-434. (preprint)
• E Byrnes, P Carter, A Doelman, and L Liu.
  Large amplitude radially symmetric spots and gaps in a dryland ecosystem model.
  Journal of Nonlinear Science 33(107) (2023). (preprint, arXiv)
• P Carter, A Doelman, K Lilly, E Obermayer, and S Rao.
  Criteria for the (in)stability of planar interfaces in singularly perturbed 2-component reaction-diffusion equations.
  Physica D 444 (2023), 133596. (preprint, arXiv)
• P Carter and A Champneys.
  Wiggly canards: growth of traveling wave trains through a family of fast-subsystem foci.
  Discrete and Continuous Dynamical Systems - S 15(9) (2022), pp. 2433-2466. (preprint)
• P Carter, J Rademacher, and B Sandstede.
  Pulse replication and accumulation of eigenvalues.
  SIAM Journal on Mathematical Analysis 53(3) (2021), pp. 3520-3576. (preprint)
• A Bauer and P Carter.
  Existence of transonic solutions in the stellar wind problem with viscosity and heat conduction.
  SIAM Journal on Applied Dynamical Systems 20(1) (2021), pp. 262-298. (preprint)
• P Carter.
  Spike-adding canard explosion in a class of square-wave bursters.
  Journal of Nonlinear Science 30(6) (2020), pp. 2613-2669. (preprint)
• T Aougab, M Beck, P Carter, S Desai, B Sandstede, M Stadt, and A Wheeler.
  Isolas versus snaking of localized rolls.
  Journal of Dynamics and Differential Equations 31(3) (2019), pp. 1199-1222. (preprint)
• J Bramburger, D Altschuler, C Avery, T Sangsawang, M Beck, P Carter, and B Sandstede.
  Localized radial roll patterns in higher space dimensions.
  SIAM Journal on Applied Dynamical Systems 18(3) (2019), pp. 1420-1453. (preprint)
• R Bastiaansen, P Carter, and A Doelman.
  Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems.
  Nonlinearity 32(8) (2019), pp. 2759-2814. (preprint)
• P Carter and A Doelman.
  Traveling stripes in the Klausmeier model of vegetation pattern formation.
  SIAM Journal on Applied Mathematics 78(6) (2018), pp. 3213-3237. (preprint)
• P Carter and A Scheel.
  Wave train selection by invasion fronts in the FitzHugh-Nagumo equation.
  Nonlinearity 31(12) (2018), pp. 5536-5572. (preprint)
• P Carter and B Sandstede.
  Unpeeling a homoclinic banana in the FitzHugh-Nagumo system.
  SIAM Journal on Applied Dynamical Systems 17(1) (2018), pp. 236-349. (preprint)
• C Xia, C Cochrane, J DeGuire, G Fan, E Holmes, M McGuirl, P Murphy, J Palmer, P Carter, L Slivinski, and B Sandstede.
  Assimilating Eulerian and Lagrangian data in traffic-flow models.
  Physica D 346 (2017), pp. 59-72. (preprint)
• P Carter, E Knobloch, and M Wechselberger.
  Transonic canards and stellar wind.
  Nonlinearity 30(3) (2017), pp. 1006-1033. (preprint)
• P Carter, B de Rijk, and B Sandstede.
  Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system.
  Journal of Nonlinear Science 26(5) (2016), pp. 1369-1444. (preprint)
• P Carter and B Sandstede.
  Fast pulses with oscillatory tails in the FitzHugh-Nagumo system.
  SIAM Journal on Mathematical Analysis 47(5) (2015), pp. 3393-3441. (preprint)
• P Carter, PL Christiansen, YB Gaididei, C Gorria, B Sandstede, MP Sorensen, and J Starke.
  Multi-jam solutions in traffic models with velocity-dependent driver strategies.
  SIAM Journal on Applied Mathematics 74(6) (2014), pp. 1895-1918. (preprint)

Conference proceedings/reports

• P Carter.
  Pulse replication and slow absolute spectrum in the FitzHugh-Nagumo system.
  Oberwolfach Reports 37 (2021), pp. 45-48.

Articles aimed at undergraduates

• P Carter, Y. Solomon.
  Relaxing the integral test: an "elementary" challenge for the advanced calculus student.
  College Mathematics Journal 48(4) (2017), pp. 290-291. (preprint)
• P Carter, D Lowry-Duda.
  On functions whose mean value abscissas are midpoints, with connections to harmonic functions.
  The American Mathematical Monthly 124(6) (2017), pp. 535-542. (preprint)

Theses

• P Carter
  Fast pulses with oscillatory tails in the FitzHugh-Nagumo system.
  PhD Thesis, Brown University, 2016
• P Carter
  Lagrangian submanifolds of Euclidean space.
  Part III Essay, University of Cambridge, 2011

Google Scholar | MathSciNet | ORCID