Related papers: Evaluating the Evans function: Order reduction in …
The Evans function is a tool for assessing the stability of travelling wave solutions for partial differential equations. A recent paper (math.NA/0605581) analyzes the order reduction experienced when evaluating the Evans function…
The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been…
In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector form of the discrete nonlinear Schrodinger…
The Evans function is an analytic function that encodes information about the intersection of certain subspaces in ODE boundary value problems. As such it is a useful tool for computing the spectrum of boundary value problems arising in the…
We perform error analyses explaining some previously mysterious phenomena arising in numerical computation of the Evans function, in particular (i) the advantage of centered coordinates for exterior product and related methods, and (ii) the…
The Evans function has become a standard tool in the mathematical study of nonlinear wave stability. In particular, computation of its zero set gives a convenient numerical method for determining the point spectrum of the associated linear…
The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…
Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier--Stokes…
We present a numerical method for computing the pure-point spectrum associated with the linear stability of multi-dimensional travelling fronts to parabolic nonlinear systems. Our method is based on the Evans function shooting approach.…
It has long been a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the principal aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such…
We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an…
In the spectral stability analysis of localized patterns to singular perturbed evolution problems, one often encounters that the Evans function respects the scale separation. In such cases the Evans function of the full linear stability…
We establish one-dimensional spectral stability of small amplitude viscous and relaxation shock profiles using Evans function techniques to perform a series of reductions and normal forms to reduce to the case of the scalar Burgers…
As described in the classic works of Lee--Stewart and Short--Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem of considerable interest in applications. Reexamining this…
Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied from the experimental, the theoretical, and the numerical perspective. From the mathematical point of view, these waves are…
We establish instability of periodic traveling waves arising in conservation laws featuring phase transition. The analysis uses the Evans function framework introduced by R.A. Gardner in the periodic case. The main new tool is a periodic…
Continuing the program initiated by Humpherys, Lyng, & Zumbrun [17] for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analyze the spectral stability of weak detonation waves in a…
We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile ofthe elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the…