Björn Sandstede, Publications
- M Beck, J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht.
Snakes, ladders, and isolas of localised patterns. PDF
Peer-Reviewed Journal Articles
- A Doelman, B Sandstede, A Scheel and G Schneider.
The dynamics of modulated wave trains.
Memoirs of the American Mathematical Society (accepted). PDF
- DJB Lloyd, B Sandstede, D Avitabile and AR Champneys.
Localized hexagon patterns of the planar Swift-Hohenberg equation.
SIAM Journal on Applied Dynamical Systems (at press).
PDF Hexagon movie Ladder movie
- G Derks, S Maad and B Sandstede.
Perturbations of embedded eigenvalues for the bilaplacian on a cylinder.
Discrete and Continuous Dynamical Systems A 21 (2008) 801-821. PDF
- B Sandstede and A Scheel.
Hopf bifurcation from viscous shock waves.
SIAM Journal on Mathematical Analysis 39 (2008) 2033-2052. DOI
- N Kutz and B Sandstede.
Theory of passive harmonic mode-locking using waveguide arrays.
Optics Express 16 (2008) 636-650. DOI
- B Sandstede and A Scheel.
Relative Morse indices, Fredholm indices, and group velocities.
Discrete and Continuous Dynamical Systems A 20 (2008) 139-158. PDF
- B Sandstede.
Evans functions and nonlinear stability of travelling waves in neuronal network models.
International Journal of Bifurcation and Chaos 17 (2007) 2693-2704. DOI
- B Sandstede and A Scheel.
Period doubling of spiral waves and defects.
SIAM Journal on Applied Dynamical Systems 6 (2007) 494-547. DOI
- A Ghazaryan and B Sandstede.
Nonlinear convective instability of Turing-unstable fronts near onset: A case study.
SIAM Journal on Applied Dynamical Systems 6 (2007) 319-347. DOI
- JDM Rademacher, B Sandstede and A Scheel.
Computing absolute and essential spectra using continuation.
Physica D 229 (2007) 166-183. DOI
- J Humpherys, B Sandstede and K Zumbrun.
Efficient computation of analytic bases in Evans function analysis of large systems.
Numerische Mathematik 103 (2006) 631-642. DOI
- B Sandstede and A Scheel.
Curvature effects on spiral spectra: Generation of point eigenvalues near branch points.
Physical Review E 73 (2006) 016217. DOI
- G Samaey and B Sandstede.
Determining stability of pulses for partial differential equations with time delays.
Dynamical Systems 20 (2005) 201-222. DOI
- T Kapitula, PG Kevrekidis and B Sandstede.
Addendum: Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems.
Physica D 201 (2005) 199-201. DOI
- E Grenier, CKRT Jones, F Rousset and B Sandstede.
Viscous perturbations of marginally stable Euler flow and finite-time Melnikov theory.
Nonlinearity 18 (2005) 465-483. DOI
- B Sandstede and A Scheel.
Basin boundaries and bifurcations near convective instabilities: A case study.
Journal of Differential Equations 208 (2005) 176-193. DOI
- B Sandstede and A Scheel.
Absolute instabilities of standing pulses.
Nonlinearity 18 (2005) 331-378. DOI
- T Kapitula, N Kutz and B Sandstede.
The Evans function for nonlocal equations.
Indiana University Mathematics Journal 53 (2004) 1095-1126. DOI
- T Kapitula, PG Kevrekidis and B Sandstede.
Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems.
Physica D 195 (2004) 263-282. DOI
- MD Groves and B Sandstede.
A plethora of three-dimensional periodic travelling gravity-capillary water waves with multipulse transverse profiles.
Journal of Nonlinear Science 14 (2004) 297-340. DOI
- B Sandstede and A Scheel.
Evans function and blow-up methods in critical eigenvalue problems.
Discrete and Continuous Dynamical Systems 10 (2004) 941-964.
- B Sandstede and A Scheel.
Defects in oscillatory media: toward a classification.
SIAM Journal on Applied Dynamical Systems 3 (2004) 1-68. DOI
- A Doelman, B Sandstede, A Scheel and G Schneider.
Propagation of hexagonal patterns near onset.
European Journal of Applied Mathematics 14 (2003) 85-110. DOI
- J Härterich, B Sandstede and A Scheel.
Exponential dichotomies for linear non-autonomous functional differential equations of mixed type.
Indiana University Mathematics Journal 51 (2002) 1081-1109. DOI
- J O’Neil, N Kutz and B Sandstede.
Theory and simulations of the dynamics and stability of actively modelocked lasers.
IEEE Journal of Quantum Electronics 38 (2002) 1412-1419. DOI
- T Kapitula, N Kutz and B Sandstede.
Stability of pulses in the master-modelocking equation.
Journal of the Optical Society of America B 19 (2002) 740-746.
- T Kapitula and B Sandstede.
Edge bifurcations for near integrable systems via Evans function techniques.
SIAM Journal on Mathematical Analysis 33 (2002) 1117-1143. DOI
- B Sandstede and A Scheel.
On the structure of spectra of modulated travelling waves.
Mathematische Nachrichten 232 (2001) 39-93. DOI
- R Moore, WL Kath, B Sandstede, CKRT Jones and JC Alexander.
Stability of multiple pulses in optical fibers with phase-sensitive amplification and noise.
Optics Communications 195 (2001) 127-139. DOI
- B Sandstede and A Scheel.
Essential instabilities of fronts: bifurcation, and bifurcation failure.
Dynamical Systems 16 (2001) 1-28. DOI
- B Sandstede and A Scheel.
On the stability of periodic travelling waves with large spatial period.
Journal of Differential Equations 172 (2001) 134-188. DOI
- B Sandstede and A Scheel.
Superspiral structures of meandering and drifting spiral waves.
Physical Review Letters 86 (2001) 171-174. DOI
- B Sandstede and A Scheel.
Absolute and convective instabilities of waves on unbounded and large bounded domains.
Physica D 145 (2000) 233-277. DOI
- B Sandstede and A Scheel.
Absolute versus convective instability of spiral waves.
Physical Review E 62 (2000) 7708-7714. DOI
- B Sandstede.
Center manifolds for homoclinic solutions.
Journal of Dynamics and Differential Equations 12 (2000) 449-510. DOI
- B Sandstede and A Scheel.
Gluing unstable fronts and backs together can produce stable pulses.
Nonlinearity 13 (2000) 1465-1482. DOI
- B Sandstede, S Balasuriya, CKRT Jones and P Miller.
Melnikov theory for finite-time vector fields.
Nonlinearity 13 (2000) 1357-1377. DOI
- GJ Lord, D Peterhof, B Sandstede and A Scheel.
Numerical computation of solitary waves in infinite cylindrical domains.
SIAM Journal on Numerical Analysis 37 (2000) 1420-1454. DOI
- B Sandstede and A Scheel.
Spectral stability of modulated travelling waves bifurcating near essential instabilities.
Proceedings of the Royal Society of Edinburgh A 130 (2000) 419-448. DOI
- AC Yew, B Sandstede and CKRT Jones.
Instability of multiple pulses in coupled nonlinear Schrödinger equations.
Physical Review E 61 (2000) 5886-5892. DOI
- B Sandstede and A Scheel.
Essential instability of pulses and bifurcations to modulated travelling waves.
Proceedings of the Royal Society of Edinburgh A 129 (1999) 1263-1290.
- D Peterhof and B Sandstede.
All-optical clock recovery using multisection distributed-feedback lasers.
Journal of Nonlinear Science 9 (1999) 575-613. DOI
- B Sandstede, A Scheel and C Wulff.
Bifurcations and dynamics of spiral waves.
Journal of Nonlinear Science 9 (1999) 439-478. DOI
- T Kapitula and B Sandstede.
Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations.
Physica D 124 (1998) 58-103. DOI
- T Kapitula and B Sandstede.
Instability mechanism for bright solitary-wave solutions to the cubic-quintic Ginzburg-Landau equation.
Journal of the Optical Society of America B 15 (1998) 2757-2762.
- U Bandelow, L Recke and B Sandstede.
Frequency regions for forced locking of self-pulsating multi-section DFB lasers.
Optics Communications 147 (1998) 212-218. DOI
- S Balasuriya, CKRT Jones and B Sandstede.
Viscous perturbations of vorticity-conserving flows and separatrix splitting.
Nonlinearity 11 (1998) 47-77. DOI
- B Sandstede.
Stability of multiple-pulse solutions.
Transactions of the American Mathematical Society 350 (1998) 429-472. DOI
- B Sandstede.
Stability of N-fronts bifurcating from a twisted heteroclinic loop and an application to the FitzHugh-Nagumo equation.
SIAM Journal on Mathematical Analysis 29 (1998) 183-207. DOI
- B Sandstede, A Scheel and C Wulff.
Dynamics of spiral waves on unbounded domains using center-manifold reductions.
Journal of Differential Equations 141 (1997) 122-149. DOI
- D Peterhof, B Sandstede and A Scheel.
Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders.
Journal of Differential Equations 140 (1997) 266-308. DOI
- B Sandstede.
Instability of localized buckling modes in a one-dimensional strut model.
Philosophical Transactions of the Royal Society of London A 355 (1997) 2083-2097. DOI
- B Sandstede.
Convergence estimates for the numerical approximation of homoclinic solutions.
IMA Journal of Numerical Analysis 17 (1997) 437-462. DOI
- B Sandstede, CKRT Jones and JC Alexander.
Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers.
Physica D 106 (1997) 167-206. DOI
- B Sandstede.
Constructing dynamical systems having homoclinic bifurcation points of codimension two.
Journal of Dynamics and Differential Equations 9 (1997) 269-288. DOI
- JC Alexander, MG Grillakis, CKRT Jones and B Sandstede.
Stability of pulses on optical fibers with phase-sensitive amplifiers.
Zeitschrift für Angewandte Mathematik und Physik 48 (1997) 175-192. DOI
- B Sandstede, A Scheel and C Wulff.
Center-manifold reduction for spiral waves.
Comptes Rendus de l’Académie des Sciences I 324 (1997) 153-158.
- M Krupa, B Sandstede and P Szmolyan.
Fast and slow waves in the FitzHugh-Nagumo equation.
Journal of Differential Equations 133 (1997) 49-97. DOI
- B Fiedler, B Sandstede, A Scheel and C Wulff.
Bifurcation from relative equilibria of noncompact group actions: skew products, meanders, and drifts.
Documenta Mathematica 1 (1996) 479-505. PDF
- AR Champneys, YA Kuznetsov and B Sandstede.
A numerical toolbox for homoclinic bifurcation analysis.
International Journal of Bifurcation and Chaos 6 (1996) 867-887. DOI
- AR Champneys, J Härterich and B Sandstede.
A non-transverse homoclinic orbit to a saddle-node equilibrium.
Ergodic Theory & Dynamical Systems 16 (1996) 431-450.
- B Sandstede and A Scheel.
Forced symmetry breaking of homoclinic cycles.
Nonlinearity 8 (1995) 333-365. DOI
- B Sandstede and B Fiedler.
Dynamics of periodically forced parabolic equations on the circle.
Ergodic Theory & Dynamical Systems 12 (1992) 559-571.
- P Brunovský, P Polácik and B Sandstede.
Convergence in general periodic parabolic equations in one space dimension.
Nonlinear Analysis (Theory, Methods & Applications) 18 (1992) 209-215. DOI
Review Articles
- AR Champneys and B Sandstede.
Numerical computation of coherent structures.
In: Numerical Continuation Methods for Dynamical Systems (B Krauskopf, HM Osinga and J Galan-Vioque, eds.).
Springer (2007) 331-358. PDF
- B Sandstede.
The Evans function.
In: Encyclopedia of Nonlinear Science (A Scott, ed.).
Routledge (2005) 278-279.
- T Kapitula and B Sandstede.
Eigenvalues and resonances using the Evans function.
Discrete and Continuous Dynamical Systems A 10 (2004) 857-869.
- WJ Beyn, A Champneys, E Doedel, W Govaerts, YA Kuznetsov and B Sandstede.
Numerical continuation, and computation of normal forms.
In: Handbook of Dynamical Systems II (B Fiedler, ed.).
North-Holland (2002) 149-219.
- B Sandstede.
Stability of travelling waves.
In: Handbook of Dynamical Systems II (B Fiedler, ed.).
North-Holland (2002) 983-1055. PDF
- B Sandstede, A Scheel and C Wulff.
Dynamical behavior of patterns with Euclidean symmetry.
In: Pattern Formation in Continuous and Coupled Systems (M Golubitsky, D Luss and S Strogatz, eds.).
Springer, IMA Volumes in Mathematics and its Applications 115 (1999) 249-264.
Contributions to Conference Proceedings
- B Sandstede and A Scheel.
Absolute and convective stability in large domains.
In: International Conference on Differential Equations, Berlin 1999.
World Sci. Publishing 1 (2000) 797-800.
- R Moore, WL Kath, B Sandstede, CKRT Jones and JC Alexander.
Stable multiple pulses in optical fibers with phase-sensitive amplification.
In: Nonlinear guided waves and their applications.
Optical Society of America, Technical Digest Series 5 (1998) 264-266.
- D Peterhof, L Recke and B Sandstede.
On frequency locking of self-pulsating two-section DFB lasers.
In: Self-organization in activator-inhibitor systems: semiconductors, gas-discharge and chemical active media (H Engel, FJ Niedernostheide, HG Purwins and E Schöll, eds.).
Wissenschaft und Technik Verlag (1996) 218-222.
- B Sandstede.
Asymptotic behavior of solutions of nonautonomous scalar reaction-diffusion equations.
In: International Conference on Differential Equations, Barcelona 1991 (C Perello, C Simo and J Sola-Morales, eds.).
World Sci. Publishing 2 (1993) 888-892.
Technical Reports
- E Doedel, RC Paffenroth, AR Champneys, TF Fairgrieve, YA Kuznetsov, BE Oldeman, B Sandstede and X Wang.
AUTO2000: Continuation and bifurcation software for ordinary differential equations (with HOMCONT).
Technical report, Concordia University, 2002. PDF
- E Doedel, AR Champneys, TF Fairgrieve, YA Kuznetsov, B Sandstede and X Wang.
AUTO97: Continuation and bifurcation software for ordinary differential equations (with HOMCONT).
Technical report, Concordia University, 1997. PDF
- AR Champneys, YA Kutznetsov and B Sandstede.
HOMCONT: An AUTO86 driver for homoclinic bifurcation analysis (Version 2.0).
Technical Report AM-R9516, CWI Amsterdam, 1995. PDF
Theses
- B Sandstede.
Verzweigungstheorie homokliner Verdopplungen.
PhD thesis, University of Stuttgart, 1993. PDF
- B Sandstede.
Omega-Limesmengen von Lösungen eindimensionaler Wärmeleitungsgleichungen mit periodischer Zeitabhängigkeit.
Master’s thesis, University of Heidelberg, 1990.
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