WAVETRAIN is a free, open-source software package for investigating periodic travelling wave solutions of partial differential equations. Typically such equations will contain a number of parameters. WAVETRAIN requires that one of these be selected; this parameter is referred to as the control parameter. Focussing on periodic travelling waves introduces an additional parameter, the wave speed. The basic task performed by WAVETRAIN is the calculation of the region of the control parameter - wave speed plane in which periodic travelling waves exist, and additionally where they are stable. WAVETRAIN’s calculations all use the method of numerical continuation. WAVETRAIN is intended to be easy to use, even for users with limited mathematical/computational background. In particular, the input files for WAVETRAIN are all simple text files: users are not required to write any computer programs, and do not need expertise in any programming language or other software. WAVETRAIN includes a plotter to visualise the results of its calculations. WAVETRAIN plots are publication-quality, and can be fine-tuned by the user if required. WAVETRAIN also provides detailed output data files that are accessible to the user if required, and that have an easily comprehensible format.

References in zbMATH (referenced in 22 articles , 1 standard article )

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  1. Lloyd, David J.: Hexagon invasion fronts outside the homoclinic snaking region in the planar Swift-Hohenberg equation (2021)
  2. Sherratt, Jonathan A.; Liu, Quan-Xing; van de Koppel, Johan: A comparison of the “reduced losses” and “increased production” models for mussel bed dynamics (2021)
  3. Eigentler, L.; Sherratt, J. A.: Spatial self-organisation enables species coexistence in a model for savanna ecosystems (2020)
  4. Eigentler, Lukas; Sherratt, Jonathan A.: An integrodifference model for vegetation patterns in semi-arid environments with seasonality (2020)
  5. Bennett, Jamie J. R.; Sherratt, Jonathan A.: Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts (2019)
  6. Bennett, Jamie J. R.; Sherratt, Jonathan A.: Large scale patterns in mussel beds: stripes or spots? (2019)
  7. Lloyd, David J. B.: Invasion fronts outside the homoclinic snaking region in the planar Swift-Hohenberg equation (2019)
  8. Gani, M. Osman; Ogawa, Toshiyuki: Spiral breakup in a RD system of cardiac excitation due to front-back interaction (2018)
  9. Sun, Xianbo; Yu, Pei; Qin, Bin: Global existence and uniqueness of periodic waves in a population model with density-dependent migrations and allee effect (2017)
  10. Vidal-Henriquez, Estefania; Zykov, Vladimir; Bodenschatz, Eberhard; Gholami, Azam: Convective instability and boundary driven oscillations in a reaction-diffusion-advection model (2017)
  11. Gani, M. Osman; Ogawa, Toshiyuki: Stability of periodic traveling waves in the Aliev-Panfilov reaction-diffusion system (2016)
  12. Sherratt, J. A.: Using numerical bifurcation analysis to study pattern formation in mussel beds (2016)
  13. Sherratt, Jonathan A.: Invasion generates periodic traveling waves (wavetrains) in predator-prey models with nonlocal dispersal (2016)
  14. Sherratt, Jonathan A.; Mackenzie, Julia J.: How does tidal flow affect pattern formation in mussel beds? (2016)
  15. Gani, M. Osman; Ogawa, Toshiyuki: Instability of periodic traveling wave solutions in a modified Fitzhugh-Nagumo model for excitable media (2015)
  16. Innocenti, Giacomo; Paoletti, Paolo: Embedding dynamical networks into distributed models (2015)
  17. Wang, Qinlong; Huang, Wentao: Limit periodic travelling wave solution of a model for biological invasions (2014)
  18. Sherratt, Jonathan A.: Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. IV: Slowly moving patterns and their stability (2013)
  19. Sherratt, Jonathan A.: Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations (2013)
  20. Tresaco, E.; Riaguas, A.; Elipe, A.: Numerical analysis of periodic solutions and bifurcations in the planetary annulus problem (2013)

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