相关论文: Heteroclinic orbits, mobility parameters and stabi…

We study standing periodic waves modeled by the nonlinear Schrodinger equation with the intensity-dependent dispersion coefficient. Spatial periodic profiles are smooth if the frequency of the standing waves is below the limiting frequency,…

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u^4+au^2-u+f(u,b)=0 as a model. Here f is an analytic function and a, b real parameters. These equations are…

The concept of stability has a long history in the field of dynamical systems: stable invariant objects are the ones that would be expected to be observed in experiments and numerical simulations. Heteroclinic networks are invariant objects…

In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different…

Locating the position of periodic orbits in galaxies is undoubtedly an issue of paramount importance. We reveal the position and the stability of periodic orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric…

Steady states of the thin film equation $u_t+[u^3 (u_xxx + \alpha^2 u_x -\sin(x) )]_x=0$ are considered on the periodic domain $\Omega = (-\pi,\pi)$. The equation defines a generalized gradient flow for an energy functional that controls…

Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of…

We give a complete description of the shapes and the behavior of all homoclinic orbits in the Euler problem of two fixed centers.

Within the Landau-like approach we study anomalies of elastic moduli at phase transitions in thin films on substrates. We consider the case where, similar to many experimental cases, the first-order transition in free crystal would convert…

In this work, the interplay between non-Hermiticity, quasi-disorder, and repulsive interaction is studied for hard-core bosons confined in a one-dimensional optical lattice, where non-Hermiticity is induced by the non-reciprocal hoppings…

This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…

The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose…

The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…

In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally…

In this paper we analyze a generic dynamical system with $\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from…

We study the critical phenomena of the dynamical transition from a metastable state to a stable state in the model of first-order phase transition via two different triggering mechanisms. Three universal stages during the fully nonlinear…

Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…

Transition-metal oxides have been a central subject of condensed matter physics for decades. In addition to novel electronic states driven by the influence of strong correlation, relativistic spin-orbit coupling effects have recently…

We study generic two- and three-parameter unfoldings of a pair of orbits of quadratic homoclinic tangency in strongly dissipative systems. We prove that the corresponding stability windows for periodic orbits have various universal forms:…