1 - 10 of 11 articles
The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period T yet mimic with good approximation, or even exactly, any given many-body problem (within a quite large...
We describe some recent results on existence of quasi-periodic solutions of Hamiltonian PDEs on compact manifolds. We prove a linear stability result for the non-linear Schrödinger equation in the case of SU(2) and SO(3).
This paper presents an introduction to the existence and stability of stationary fronts in wave equations with finite length spatial inhomogeneities. The main focus will be on wave equations with one or two inhomogeneities. It will be shown that the fronts come in families. The front solutions...
Rearrangement of rotation-vibration energy bands in isolated molecules within semi-quantum approach is characterized by delta-Chern invariants, each of which is associated to a locally approximated semi-quantum Hamiltonian valid in a small neighborhood of a degeneracy point for the initial...
The purpose of this article is to introduce the reader to phenomena on time-varying spatial domains and to highlight the differences from their counterpart on time-fixed domains. We begin by discussing the origin of this class of problems in various physical systems and applications, and then...
We review essential techniques in the study of families of periodic orbits of slow-fast systems in the plane. The techniques are demonstrated by treating orbits passing through unfoldings of transcritical intersections of curves of singular points in the most generic setting. We show that such...
We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors.
We collect classical and more recent material about possible symplectic descriptions of the phase space of the planetary problem.
We determine locally minimizing functions that are invariant with respect to the action of a finite linear group. This resolves a problem which is inverse to one discussed in a seminal paper by Abud and Sartori, and occurs naturally in various physical applications, such as elasticity theory and...
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