pde2path - a Matlab package for continuation and bifurcation in systems of PDEs

Home | Tutorials | Applications| Backlog


Here we give a list of selected applications of pde2path beyond the demos.

  1. H. Uecker and D. Wetzel, Numerical results for snaking of patterns over patterns in some 2D Selkov-Schnakenberg Reaction-Diffusion systems, SIADS, 13-1:94-128, 2014; Preprint, Movies
  2. D. Zhelyazov, D. Han-Kwan, and J. Rademacher, Global stability and local bifurcations in a two-fluid model for a Tokamak plasma, SIADS, 14,2:730-763, 2015
  3. C. Kuehn, Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs, Appl. Math. Comput, 266, 656-674, 2015
  4. C. Kuehn, Numerical continuation and SPDE stability for the 2D cubic-quintic Allen-Cahn equation, SIAM/ASA J. Uncertain. Quantif., 2015:3, 762-789
  5. E. Siero, A. Doelman, M. B. Eppinga, J. D. M. Rademacher, M. Rietkerk, and K. Siteur, Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes, Chaos 25, 036411 (2015)
  6. D. Wetzel, Pattern analysis in a benthic bacteria-nutrient system, Math. Biosci. Eng., 13:303-332, 2016
  7. H. Uecker, Optimal harvesting and spatial patterns in a semi arid vegetation system, Natural Resource Modeling, 29-2:229-258, 2016, Preprint
  8. T. Dohnal and H. Uecker, Bifurcation of Nonlinear Bloch waves from the spectrum in the nonlinear Gross-Pitaevskii equation, J. Nonlinear Sci. 26:3, 581-618, Preprint
  9. S. Engelnkemper, M. Wilczek, S. Gurevich, and U. Thiele, Morphological Transitions of Sliding Drops - Dynamics and Bifurcations, Phys. Rev. Fluids, 1:7, 073901, 2016
  10. Y. Zelnik, H. Uecker, U. Feudel, and E. Meron, Desertification by Front Propagation?, J.Theor.Biology, 418:27-35, 2017, Preprint
  11. D. Grass and H. Uecker, Optimal management and spatial patterns in a distributed shallow lake model, EJDE, 2017:1, 1-21, 2017, Preprint
  12. H. Uecker and T. Upmann, Optimal fishery with coastal catch, Preprint, 2017
  13. T. Dohnal and P. Siegl, Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry, J. Math. Phys 57:093502, 2016.
  14. S. Bier, N. Gavish, H. Uecker, and A. Yochelis, Mean field approach to first and second order phase transitions in ionic liquids, PRE rapid communications, 2017, Preprint
  15. M. Wilczek, W. Tewes, S. Engelnkemper, S. Gurevich, U. Thiele, Sliding drops - ensemble statistics from single drop bifurcations, Preprint, 2017
  16. S. V. Gurevich, J. Javaloyes, Spatial instabilities of light bullets in passively-mode-locked lasers, PRA 96, 023821, 2017
  17. C Schelte, J Javaloyes, SV Gurevich, Dynamics of Temporal Localized States in Passively Mode-Locked Semiconductor Lasers, Preprint, 2017
  18. N. Gavish, Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions, Physica D, 2018
  19. D. Wetzel, Tristability between stripes, up-hexagons, and down-hexagons and snaking bifurcation branches of spatial connections between up- and down-hexagons, PRE, 97, 2018.
  20. S. Engelnkemper, S. V. Gurevich, H. Uecker, D. Wetzel, U. Thiele, Continuation for thin film hydrodynamics and related scalar problems, in Comput. Methods Appl. Sci., 50, Springer, Cham, 2019, preprint