Publications - Arnd Scheel

Preprints Refereed Journals Review Articles Proceedings Theses Home


Preprints

R. Goh, S. Mesuro, A. Scheel
Coherent structures in reaction-diffusion models for precipitation (PDF)

A. Pogan, A. Scheel
Instability of Spikes in the Presence of Conservation Laws (PDF)

A. Pogan, A. Scheel
Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity (PDF)

Refereed Journals

J. Bellay, A. Scheel
Coherent structures near the boundary between excitable and oscillatory media (PDF)
Dyn. Syst., to appear.

T. Gallay, A. Scheel
Diffusive stability of oscillations in reaction-diffusion systems (PDF)
Trans. Amer. Math. Soc., to appear.

A. Scheel, E. van Vleck
Lattice differential equations embedded into reaction-diffusion systems (PDF)
Proc. Royal Soc. Edinburgh A, 139A (2009), 193-207.

A. Doelman, B. Sandstede, A. Scheel, G. Schneider
The dynamics of modulated wave trains (PDF)
Mem. Amer. Math. Soc. 199 (2009).

A. Scheel
Robustness of Liesegang patterns (PDF)
Nonlinearity 22 (2009), 457-483.

J.D. Wright, A. Scheel
Colliding dissipative pulses - the shooting manifold (PDF)
J. Differential Eqns. 245 (2008), 59-79.

B. Sandstede, A. Scheel
Hopf bifurcation from viscous shock waves (PDF)
SIAM J. Math. Anal. 39 (2008), 2033-2052.

B. Sandstede, A. Scheel
Relative Morse indices, Fredholm indices, and group velocities (PDF)
Discr. Cont. Dyn. Sys. 20 (2008), 139-158.

M. Haragus, A. Scheel
Interfaces between rolls in the Swift-Hohenberg equation (PDF)
Int. J. Dyn. Sys. Diff. Eqns. 1 (2007), 89-97.

J.D.M. Rademacher, A. Scheel
Instabilities of wave trains and Turing patterns in large domains (PDF )
Int. J. Bif. Chaos 16 (2007), 2679-2691.

J.D. Wright, A. Scheel
Solitary waves and their linear stability in weakly coupled KdV equations (PDF)
Z. Angew. Math. Phys. 58 (2007), 535-570.

B. Sandstede, A. Scheel
Period-doubling of spiral waves and defects (PDF)
SIAM J. Appl. Dyn. Syst. 6 (2007), 494-547.

M. Haragus, A. Scheel
Stable viscous shocks in elliptic conservation laws (PDF)
Indiana Univ. Math. J. 56 (2007), 1261-1278.

J.D.M. Rademacher, A. Scheel
The saddle-node of nearly homogeneous wave trains in reaction-diffusion systems (PDF)
J. Dyn. Diff. Eqns. 19 (2007), 479-496.

J.D.M. Rademacher, B. Sandstede, A. Scheel
Computing absolute and essential spectra using continuation (PDF)
Physica D 229 (2007), 166-183.

R. Kollár, A. Scheel
Coherent structures generated by inhomogeneities in oscillatory media (PDF)
SIAM J. Appl. Dyn. Syst. 6 (2007), 236-262.

M. Haragus, E. Lombardi, A. Scheel
Spectral stability of wave trains in the Kawahara equation (PDF)
J. Math. Fluid Mechanics 8 (2006), 482-509.

A. Scheel
Coarsening fronts (PDF)
Archive for Rational Mechanics and Analysis 181 (2006), 505-534.

M. Haragus, A. Scheel
Almost planar waves in anisotropic media (PDF)
Comm. Partial Differential Equations 31 (2006), 791-815.

M. Haragus, A. Scheel
Corner defects in almost planar interface propagation (PDF)
Ann. Inst. H. Poincare (C) Anal. Non Lineaire 23 (2006), 283-329.

B. Sandstede and A. Scheel
Curvature effects on spiral spectra: Generation of point eigenvalues near branch points (PDF)
Phys. Rev. E 73 (2006), 016217.

B. Sandstede, A. Scheel
Basin boundaries and bifurcations near convective instabilities: A case study (PDF)
J. Diff. Eqns. 208 (2005), 176-193.

B. Sandstede, A. Scheel
Absolute instabilities of standing pulses (PDF)
Nonlinearity 18 (2005), 331-378.

B. Sandstede, A. Scheel
Evans function and blow-up methods in critical eigenvalue problems (PDF)
Discr. Cont. Dyn. Sys. 10 (2004), 941-964.

B. Sandstede, A. Scheel
Defects in oscillatory media: toward a classification (PDF)
SIAM J. Appl. Dyn. Syst. 3 (2004), 1-68.

A. Scheel
Radially symmetric patterns of reaction-diffusion systems (PDF)
Mem. Amer. Math. Soc. 165 (2003).

D.Pelinovsky, A. Scheel
Stability analysis of stationary light transmission in nonlinear photonic structures (PDF)
J. Nonlinear Science 13 (2003), 347-396..

A. Doelman, B. Sandstede, A. Scheel, and G. Schneider
Propagation of hexagonal patterns near onset (PDF)
Europ. J. Appl. Math. 14 (2003), 85-110.

K. Matthies, A. Scheel
Exponential Averaging for Hamiltonian Evolution Equations (PDF)
Trans. Amer. Math. Soc. 355 (2003), 747-773..

J. Härterich, B. Sandstede, A. Scheel
Exponential dichotomies for non-autonomous functional differential equations of mixed type (PDF)
Indiana Univ. Math. J. 51 (2002), 1081-1109.

M. Haragus, A. Scheel
Linear stability and instability of ion-acoustic plasma solitary waves (PDF)
Physica D 170 (2002), 13-30.

M. Haragus, A. Scheel
Finite-wavelength stability of capillary-gravity solitary waves (PDF)
Commun. Math. Phys. 225 (2002), 487-521.

B. Sandstede, A. Scheel
On the structure of spectra of modulated travelling waves (PDF)
Math. Nachr. 232 (2001), 39-93.

B. Sandstede, A. Scheel
Super-spiral structures of meandering and drifting spiral waves (PDF)
Phys. Rev. Lett. 86 (2001), 171-174.

B. Sandstede, A. Scheel
On the stability of periodic travelling waves with large spatial period (PDF)
J. Diff. Eqns. 172 (2001), 134-188.

B. Sandstede, A. Scheel
Essential instabilities of fronts: bifurcation and bifurcation failure (PDF)
Dynamical Systems 16 (2001), 1-28.

B. Sandstede, A. Scheel
Absolute versus convective instability of spiral waves (PDF)
Phys. Rev. E. 62 (2000), 7708-7714.

B. Sandstede, A. Scheel
Absolute and convective instabilities of waves on unbounded and large bounded domains (PDF)
Physica D 145 (2000), 233-277.

B. Sandstede, A. Scheel
Gluing unstable fronts and backs together can produce stable pulses (PDF)
Nonlinearity 13 (2000), 1465-1482.

B. Sandstede, A. Scheel
Spectral stability of modulated travelling waves bifurcating near essential instabilities (PDF)
Proc. Roy. Soc. Edinb. A 130 (2000), 419-448.

G. J. Lord, D. Peterhof, B. Sandstede, A. Scheel
Numerical computation of solitary waves in infinite cylindrical domains (PDF)
SIAM J. Numerical Analysis 37 (2000), 1420-1454.

B. Sandstede, A. Scheel
Essential instability of pulses and bifurcations to modulated travelling waves (PDF)
Proc. Roy. Soc. Edinb. A 129 (1999), 1263-1290.

B. Sandstede, A. Scheel, C. Wulff
Bifurcations and dynamics of spiral waves ( PDF)
J. Nonlinear Science 9 (1999), 439-478.

B. Fiedler, A. Scheel, M.I. Vishik
Large patterns of elliptic systems in infinite cylinders (PDF)
J. Math. Pures Appl. 77 (1998), 879-907.

A. Scheel
Bifurcation to spiral waves in reaction-diffusion systems (PDF)
SIAM J. Math. Anal. 29 (1998), 1399-1418.

A. Scheel
Subcritical bifurcation to infinitely many rotating waves (PDF)
J. Math. Anal. Appl. 215 (1997), 252-261.

B. Sandstede, A. Scheel, C. Wulff
Dynamics of spiral waves on unbounded domains using center-manifold reduction (PDF)
J. Diff. Eqns. 141 (1997), 122-149.

D. Peterhof, B. Sandstede, A. Scheel
Exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders (PDF)
J. Diff. Eqns. 140 (1997), 266-308.

B. Sandstede, A. Scheel, C. Wulff
Center manifold reduction for spiral wave dynamics (PDF)
C. R. Acad. Sci. Paris, Serie I, t.324 (1997), 153-158.

P. Chossat, M. Krupa, I. Melbourne, A. Scheel
Transverse bifurcations of homoclinic cycles (PDF)
Physica D 100 (1997) 85-100.

A. Scheel
Existence of fast travelling waves for some parabolic equations --- a dynamical systems approach. (PDF)
J. Dyn. Diff. Eqns. 8 (1996), 469-548.

B. Fiedler, B. Sandstede, A. Scheel, C. Wulff
Bifurcation from relative equilibria of noncompact group actions: skew products, meanders, and drifts (PDF)
Documenta Mathematica 1 (1996), 479-505.

B. Sandstede, A. Scheel
Forced symmetry breaking of homoclinic cycles (PDF)
Nonlinearity 8 (1995), 333-365.

A. Scheel
Fast travelling waves for convective reaction-diffusion equations
C. R. Acad. Sci. Paris, Serie I, t. 317 (1993), 347-351.

A. Scheel
Fast travelling waves for the Cahn-Hilliard equation in an infinite strip
C. R. Acad. Sci. Paris, Serie I, t. 317 (1993), 261-265.

A. Scheel, P. Chossat
Bifurcation d'orbites periodiques a partir d'un cycle homocline symetrique (PDF)
C. R. Acad. Sci. Paris, Serie I, t. 314 (1992), 49-54.

Review Articles

M. Haragus, A. Scheel
A bifurcation approach to non-planar traveling waves in reaction-diffusion systems (PDF)
GAMM-Mitt. 30, (2007), 75-95.

B. Fiedler, A. Scheel
Spatio-Temporal Dynamics of Reaction-Diffusion Patterns (PDF)
In Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, F. Tomi (Eds.), Springer-Verlag, Berlin, 2003 (145 pages).

B. Sandstede, A. Scheel, 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-Verlag. IMA Volumes in Mathematics and its Applications 115 (1999), 249-264.

Proceedings

B. Sandstede, A. Scheel
Absolute and convective stability in large domains
In Proceedings of Equadiff 99, B. Fiedler, K. Gröoger, and J. Sprekels (eds.), World Scientific Publishing, Singapore (2000), 797-800.

M. Efendiev, A. Scheel
Upper and lower bounds for the Hausdorff dimension of the attractor for reaction-diffusion equations in R\sup n
In Proceedings of ``Nonlinear evolution equations and application'', M.Otani (ed.), RIMS, Kyoto (1999), 81-90.

P. Chossat, M. Krupa, I. Melbourne, A. Scheel
Magnetic dynamos in rotating convection --- a dynamical systems approach
Dyn. Cont. Discrete Impulsive Syst. 5 (1999), 327-340.

A. Scheel
Meandering Spirals
Z. Angew. Math. Mech. 79 (1999) 163-166.

Theses

DEA INLN, Nice 1991
Bifurcation d'orbites periodiques a partir de cycles homoclines en presence de symetrie (PDF)

PhD, FU Berlin, 1994
Existence of fast travelling waves for some parabolic equations - a dynamical systems approach

Habilitation, FU Berlin, 2001
Radially symmetric patterns of reaction-diffusion systems

Arnd Scheel's Home Page
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