Related papers: The Evans function as a lower bound on the spectra…
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…
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…
We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary…
In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspaces evolving according to the associated eigenvalue ODE. For…
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…
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 is a powerful tool for the stability analysis of viscous shock profiles; zeros of this function carry stability information. In the one-dimensional case, it is typical to compute the Evans function using Goodman's…
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.…
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…
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…
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…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
The nonlinear Schr\"{o}dinger equation with a linear periodic potential and a nonlinearity coefficient $\Gamma$ with a discontinuity supports stationary localized solitary waves with frequencies inside spectral gaps, so called surface gap…
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…
Two concepts, very different in nature, have proved to be useful in analytical and numerical studies of spectral stability: (i) the Krein signature of an eigenvalue, a quantity usually defined in terms of the relative orientation of certain…
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…
Localized patterns are spatially confined structures that arise in lattice dynamical systems and play an important role in physics, biology, and materials science. While their existence and bifurcation structure are well-understood, the…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
We report on detailed investigation of the stability of localized modes in the nonlinear Schrodinger equations with a nonlinear parity-time (alias PT) symmetric potential. We are particularly focusing on the case where the…
For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions…