The study of spatial patterns in extended systems, and their evolution with time, poses
challenging questions for physicists and mathematicians alike. Waves on water, pulses in …

Publisher Summary This chapter describes Heteroclinic orbits for some classes of second
and fourth order differential equations. In qualitative theory of differential equations, a …

We establish the existence of homoclinic solutions for a class of fourth-order equations
which includes the Swift–Hohenberg model and the suspension bridge equation. In the first …

For a class of Hamiltonian systems in ℝ 4 the set of homoclinic and heteroclinic orbits which
connect saddle-focus equilibria is studied using a variational approach. The oscillatory …

We study the bounded solutions of a class of fourth-order equations− γu′′′′+ u ″+ f
(u)= 0, γ> 0. We show that when γ is not too large then the paths in the (u, u′)-plane of two …

In the first half of the paper we construct a Morse-type theory on certain spaces of braid
diagrams. We define a topological invariant of closed positive braids which is correlated with …

We consider stationary solutions of the Extended Fisher-Kolmogorov (EFK) equation, a
fourth-order model equation for bi-stable systems. We show that as long as the stable …

We propose a unified functional analytic approach to study the uniform analytic-Gevrey
regularity and the decay of solutions to semilinear elliptic equations on R n. First, we …

We consider fourth-order parabolic equations of gradient type. For the sake of simplicity, the
analysis is carried out for the specific equation u\sbt=-γ\uxxxx+βuxx-F\sp′(u) with …

We investigate periodic and chaotic solutions of Hamiltonian systems in ℝ 4 which arise in
the study of stationary solutions of a class of bistable evolution equations. Under very mild …