On the Structure of Spectra of Modulated Travelling Waves

By Bjorn Sandstede, Arnd Scheel. 2001

94 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0c16eb50ea127015afda9cdf244768cfd608641e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. John Mallet-Paret
2. Bjorn Sandstede
3. Arnd Scheel
4. J. Härterich
5. Arjen Doelman
6. Guido Schneider

In Control and Systems Engineering

1. John Mallet-Paret
2. Bjorn Sandstede
3. Arnd Scheel
4. J. Härterich
5. Arjen Doelman
6. Guido Schneider

In Numerical Analysis

1. John Mallet-Paret
2. Bjorn Sandstede
3. Arjen Doelman
4. Arnd Scheel
5. Guido Schneider
6. J. Härterich
7. V. D. Ploeg

Citations in the corpus

• Propagation of hexagonal patterns near onset (2003, methodology): “Using spatial dynamics, it is often possible to lift stability properties for Ginzburg–Landau equations back to the underlying PDE: we refer to Bridges & Mielke [3] and Mielke [33] for stability of rolls and to Schneider [43] for stability of modulating fronts (see also Sandstede & Scheel [37, 38]).”
• Computing absolute and essential spectra using continuation (2007, background): “The absolute spectrum, however, depends again only on the asymptotic states u±, but not on the boundary conditions (as long as they are separated) or the profile u∗ [14].”
• Absolute and convective instabilities of waves on unbounded and large bounded domains (2000, unknown): “However, the results can be immediately generalized to cylindrical domains with multi-dimensional bounded cross-section and to time-periodic solutions of parabolic problems using a slightly generalized notion of dichotomies and Morse indices; we refer to [27,37, 38 ] for related results.”
• Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems (2014, unknown): “Introduction Traveling wave solutions of reaction–diffusion systems have been studied intensively over the last four decades since wave phenomena are observed in many time dependent processes described by evolution equations (see Conley and Gardner [8], Dunbar [9], Gardner [12], Gourley and Ruan [15”
• Relative Morse indices, Fredholm indices, and group velocities (2007, methodology): “1The assumption in [12] that c is constant is needed only to guarantee compactness with respect to the additional independent variables.”
• The Dynamics of Modulated Wave Trains (2009, background): “Before we state the first lemma, we recall from [49] that the function”
• Exponential Dichotomies and Wiener-Hopf Factorizations for Mixed-Type Functional Differential Equations (2001, methodology): “Boundary value problem, exponential dichotomy, finite section method, Fredholm index, functional differential equation, lattice differential equation, linear skew product semiflow, WienerHopf factorization.”
• Exponential dichotomies for linear non-autonomous functional differential equations of mixed type (2002, methodology): “Now that the above two properties are established, the abstract proof in [18] applies to our situation and gives the existence of exponential dichotomies.”