This survey article reviews the theory and application of homoclinic orbits to equilibria in
reversible continuous-time dynamical systems, where the homoclinic orbit and the …

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 …

This paper considers an unfolding of a degenerate reversible 1–1 resonance (or
Hamiltonian–Hopf) bifurcation for four-dimensional systems of time reversible ordinary …

This 2003 book presents min-max methods through a study of the different faces of the
celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led …

A long structural system with an unstable (subcritical) post-buckling response that
subsequently restabilizes typically deformsin a cellular manner, with localized buckles first …

Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

In this paper, the solitary waves in coupled nonlinear Schrödinger equations are classified
into infinite families. For each of the first three families, the parameter region is specified and …

The anti-integrable limit is one of the convenient and relatively simple methods for the
construction of chaotic hyperbolic invariant sets in Lagrangian, Hamiltonian, and other …

This paper considers the existence of solitary-wave solutions of the classical waterwave
problem in the presence of surface tension. A region of Bond number-Froude number …

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