Björn Sandstede

Publications

Preprints

• J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht.
  Isolas of 2-pulse solutions in homoclinic snaking scenarios. PDF
• D Avitabile, DJB Lloyd, J Burke, E Knobloch and B Sandstede.
  To snake or not to snake in the planar Swift-Hohenberg equation. Movie 1 Movie 2 PDF
• S McCalla and B Sandstede.
  Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study. PDF
• HJ Hupkes and B Sandstede.
  Travelling pulses for the discrete FitzHugh-Nagumo system. PDF
• G Derks, S Maad and B Sandstede.
  Perturbations of embedded eigenvalues for the planar bilaplacian. PDF

Peer-Reviewed Journal Articles

• M Beck, HJ Hupkes, B Sandstede and K Zumbrun.
  Nonlinear stability of semidiscrete shocks for two-sided schemes.
  SIAM Journal on Mathematical Analysis (accepted). PDF
• M Beck, B Sandstede and K Zumbrun.
  Nonlinear stability of time-periodic viscous shocks.
  Archive for Rational Mechanics and Analysis (at press). DOI
• M Oh and B Sandstede.
  Evans functions for periodic waves on infinite cylindrical domains.
  Journal of Differential Equations. 248 (2010) 544-555. DOI
• V Manukian, N Costanzino, CKRT Jones and B Sandstede.
  Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations.
  Journal of Dynamics and Differential Equations 21 (2009) 607-622. DOI
• HJ Hupkes and B Sandstede.
  Modulated wave trains in lattice differential systems.
  Journal of Dynamics and Differential Equations 21 (2009) 417-485. DOI
• V Manukian and B Sandstede.
  Multi-hump pulses in systems with reflection and phase invariance.
  Journal of Differential Equations 247 (2009) 1866-1898. DOI
• M Beck, J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht.
  Snakes, ladders, and isolas of localised patterns.
  SIAM Journal on Mathematical Analysis 41 (2009) 936-972. DOI
• A Doelman, B Sandstede, A Scheel and G Schneider.
  The dynamics of modulated wave trains.
  Memoirs of the American Mathematical Society 199(934) (2009). PDF
• M Beck, A Ghazaryan and B Sandstede.
  Nonlinear convective stability of travelling fronts near Turing and Hopf instabilities.
  Journal of Differential Equations 246 (2009) 4371-4390. DOI
• BG Bale, N Kutz and B Sandstede.
  Optimizing waveguide array mode-locking for high-power fiber lasers.
  Journal of Selected Topics in Quantum Electronics 15 (2009) 210-231. DOI
• DJB Lloyd and B Sandstede.
  Localized radial solutions of the Swift-Hohenberg equation.
  Nonlinearity 22 (2009) 485-524. DOI
• DJB Lloyd, B Sandstede, D Avitabile and AR Champneys.
  Localized hexagon patterns of the planar Swift-Hohenberg equation.
  SIAM Journal on Applied Dynamical Systems 7 (2008) 1049-1100. DOI
• 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. DOI
• 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. DOI
• 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. DOI
• 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. DOI
• 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. DOI
• 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

• AJ Homburg and B Sandstede.
  Homoclinic and heteroclinic bifurcations in vector fields.
  Handbook of Dynamical Systems III (accepted). PDF
• 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.

• Björn Sandstede
• Brown University
• 182 George Street
• Providence, RI 02912, USA