Research

Research interests

  • Exact analytic and numerical methods for ODEs, PDEs and differential equations with delays.
  • Characterisation of periodic solutions in delayed differential equations.
  • Geometry of first-order quasilinear systems of PDEs.
  • Classification of integrable systems, integrable deformations of multidimensional dispersionless systems.
  • Nonlinear interactions of waves, rank-k solutions and the gradient catastrophe phenomenon.
  • Classical Lie symmetry methods, conditional symmetries.
  • Applications in fluid dynamics, magnetohydrodynamics and mathematical biology.

Supervision

  • Dr Emrah Haspolat (PhD, completed March 2018)
  • Dynamic and stochastic models of Arabidopsis Thaliana flowering transition.

  • Dr Adam Bridgewater (PhD, completed January 2019)
  • Mathematical description of the ultradian oscillations in the glucose-insulin regulatory system.

  • Mr Jafar Masri (PhD, co-supervision with Laurent Dala)

Publications: ArXiV  Web of Knowledge

  • Bridgewater, A., Stringer, B., Huard, B., & Angelova, M., Ultradian rhythms in glucose regulation: A mathematical assessment, AIP Conference Proceedings, 2090 (2019), p. 050010.
  • Huard, B., Bridgewater, A., Angelova, M., Mathematical investigation of diabetically impaired ultradian oscillations in the glucose-insulin regulation, Journal of Theoretical Biology, 418 (2017) 66-76.
    J. Theor Biol.
  • Huard, B., Easton, J., Angelova, M., Investigation of stability in a two-delay model of the ultradian oscillations in glucose-insulin regulation, Commun Nonlinear Sci, 26 (2015) 211-222.
    Commun Nonlinear Sci
  • Huard, B., Novikov, V., On Classification of Integrable Davey-Stewartson Type Equations, J. Phys. A: Math. Theor, 46 (2013) 275202.  ArXiV   JPhysA
  • Ferapontov E.V., Huard B., Zhang A., On the central quadric ansatz: integrable models and Painleve reductions, J. Phys. A: Math. Theor, 45 (2012) 195204.  ArXiV  JPhysA
  • Grundland A.M., Huard B., Conditional symmetries and Riemann invariants for inhomogeneous hydrodynamic-type systems, J. Phys. A : Math. Theor, 43, 455217, 2010. ArXiV   JPhysA
  • Huard B., Conditionally invariant solutions of the rotating shallow water wave equations, J. Phys. A : Math. Theor, 43. 23 (2010) 235205. ArXiV   JPhysA
  • Conte R., Grundland A.M., Huard B., Elliptic solutions of isentropic ideal compressible fluid flow in (3+1) dimensions, J. Phys. A: Math. Theor. 42. 13 (2009) 135203. ArXiV   JPhysA
  • Grundland A.M., Huard B., Conditional symmetries and Riemann invariants for hyperbolic systems of PDEs, J. Phys. A: Math. Theor. 40 (2007) 4093-4123. ArXiV   JPhysA
  • Grundland A.M., Huard B., Riemann invariants and rank-k solutions of hyperbolic systems, J. Nonlin. Math. Phys., 13, 3 (2006), 393-419. ArXiV   JNMP
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