We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of the
Kawahara equation. These solutions exhibit high-frequency instabilities when subject to …

We analyze the stability of periodic, traveling-wave solutions to the Kawahara equation and
some of its generalizations. We determine the parameter regime for which these solutions …

We study the spectra for a class of differential operators with asymptotically constant
coefficients. These operators widely arise as the linearizations of nonlinear partial …

In this paper, it is proved that the KdV-Burgers equation with a monostable source term of
Fisher–KPP type has small-amplitude periodic traveling wave solutions with finite …

We study the existence and stability of small-amplitude periodic waves emerging from fold-
Hopf equilibria in a system of one reaction–diffusion equation coupled with one ordinary …

A hyperbolic model for diffusion, nonlfnear transport (or advection) and production of a
scalar quantity, is considered. The model is based on a constitutive law of Cattaneo-Maxwell …

This paper studies both existence and spectral stability properties of bounded spatially
periodic traveling wave solutions to a large class of scalar viscous balance laws in one …

We construct a new Evans function for quasi-periodic solutions to the linearisation of the
sine-Gordon equation about a periodic travelling wave. This Evans function is written in …

Euler's equations govern the behavior of gravity waves on the surface of an incompressible,
inviscid, and irrotational fluid (water, in this case). We consider the small-amplitude, periodic …

In its original formulation the Krein matrix was used to locate the spectrum of first-order star-
even polynomial operators where both operator coefficients are nonsingular. Such operators …