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


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Applications. Here we give a list of selected applications of pde2path beyond the demos and tutorials; mostly our own work, for which pde2path directories (functions and scripts) are available upon request. At the top we list applications for which these directories are reasonably well cleaned up (almost demo like) and hence can directly be downloaded.

Applications with demo like sources
  1. F.Al Saadi, E. Knobloch, A. Meiners and H. Uecker, Localized steady and oscillatory states near a Turing--Hopf instability in a semiconductor model, 2024, preprint. This revisits §3 from JDMV and discusses zipping up and unzipping of branches of Turing--Hopf mixed modes; pde2path sources and reference sheet.
  2. D. Grieser, S. Held, H. Uecker, and B. Vertman, Phase transitions on manifolds with conical singularities, 2024; preprint, pde2path sources and reference sheet.
  3. H. Uecker, Continuation and bifurcation for Nonlinear PDEs - algorithms, applications, and experiments, JDMV 2021, preprint. Comprises three (classes of) demos, namely: the 3-5-Swift-Hohenberg equation on disks; Turing--Hopf mixed modes; and non-smooth dead core problems. See also tutorial and demo files.
2022-...
  1. J. Singha, H. Uecker, and E. Meron, Traveling vegetation-herbivore waves can sustain ecosystems threatened by droughts and population growth, 2024, preprint.
  2. M. A. Ferre, I. Pavithran, B. K. Bera, H. Uecker, and E. Meron, Vegetation pattern formation and community assembly under drying climate trends, 2024, preprint.
  3. F. Al-Saadi, E. Knobloch, M.Nelson and H. Uecker, Time-dependent localized patterns in a predator-prey model, Chaos , 2024. preprint. Zipping up and unzipping of branches of Turing--Hopf mixed modes.
2018-2021
  1. H. Uecker, Optimal spatial patterns in feeding, fishing and pollution, DCDS-S , 2021, preprint. Some scalar optimal control problems, including optimal patterns and optimal time-periodic states.
  2. N. Verschueren, E. Knobloch and H. Uecker, Localized and extended patterns in the cubic-quintic Swift-Hohenberg equation on a disk, PRE 104, 2021, preprint, see also JDMV for selected results and demo files.
  3. E. Knobloch, H. Uecker, and A. Yochelis, Origin of jumping oscillons in an excitable reaction-diffusion system, PRE 104, 2021, preprint.
  4. 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
  5. 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.
  6. N. Gavish, Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions, Physica D, 2018
2014-2017
  1. 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
  2. M. Wilczek, W. Tewes, S. Engelnkemper, S. Gurevich, U. Thiele, Sliding drops - ensemble statistics from single drop bifurcations, Preprint, 2017
  3. S. V. Gurevich, J. Javaloyes, Spatial instabilities of light bullets in passively-mode-locked lasers, PRA 96, 023821, 2017
  4. C Schelte, J Javaloyes, SV Gurevich, Dynamics of Temporal Localized States in Passively Mode-Locked Semiconductor Lasers, Preprint, 2017
  5. Y. Zelnik, H. Uecker, U. Feudel, and E. Meron, Desertification by Front Propagation?, J.Theor.Biology, 418:27-35, 2017, Preprint
  6. D. Grass and H. Uecker, Optimal management and spatial patterns in a distributed shallow lake model, EJDE, 2017:1, 1-21, 2017, Preprint
  7. H. Uecker and T. Upmann, Optimal fishery with coastal catch, Preprint, 2017
  8. T. Dohnal and P. Siegl, Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry, J. Math. Phys 57:093502, 2016.
  9. D. Wetzel, Pattern analysis in a benthic bacteria-nutrient system, Math. Biosci. Eng., 13:303-332, 2016
  10. H. Uecker, Optimal harvesting and spatial patterns in a semi arid vegetation system, Natural Resource Modeling, 29-2:229-258, 2016, Preprint
  11. 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
  12. S. Engelnkemper, M. Wilczek, S. Gurevich, and U. Thiele, Morphological Transitions of Sliding Drops - Dynamics and Bifurcations, Phys. Rev. Fluids, 1:7, 073901, 2016
  13. 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
  14. C. Kuehn, Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs, Appl. Math. Comput, 266, 656-674, 2015
  15. C. Kuehn, Numerical continuation and SPDE stability for the 2D cubic-quintic Allen-Cahn equation, SIAM/ASA J. Uncertain. Quantif., 2015:3, 762-789
  16. 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