相关论文: Time-dependent finite-dimensional dynamical system…
Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition.…
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…
We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein-Gordon equation \begin{align} \partial_t^2 U - \Delta U + m^2 U = \Gamma (x) U^3 \quad \text{on } \mathbb{R} \times \mathbb{R}^3, \end{align} which are…
We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These solutions are obtained from critical points of a dual functional and they are weakly localized in space. Our abstract…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
We prove the existence of time-periodic solutions and spatially localised solutions (breathers), in general nonlinear Klein-Gordon infinite lattices. The existence problem is converted into a fixed point problem for an operator on some…
The formation and evolution of stationary and moving breather solutions in (2+1)-dimensional O(3) nonlinear $\sigma$-model are investigated. The analytical form of oscillating solutions for (2+1)-dimensional sine-Gordon equation, which…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
We consider the nonlinear Klein-Gordon equation $\partial_t^2u(x,t)-\partial_x^2u(x,t)+\alpha u(x,t)=\pm|u(x,t)|^{p-1}u(x,t)$ on a periodic metric graph (necklace graph) for $p>1$ with Kirchhoff conditions at the vertices. Under suitable…
We examine the dynamical behavior of matter coupled to gravity in the context of a linear Klein-Gordon equation coupled to a Friedman-Robertson-Walker metric. The resulting ordinary differential equations can be decoupled, the effect of…
We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional…
We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…
We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with initial data in the form of a modulated highly oscillatory exponential. In this regime of a small scaling parameter $\varepsilon$, the solution exhibits…
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems…
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
We study a new approach to generally covariant quantum mechanics applied in the case of an FLRW cosmological background. For positive spatial curvature we find a discrete series of solutions of the Klein-Gordon equation that can reasonably…
We extended the notion of Newton-Wigner localization, already constructed in the bi-dimensional de Sitter space, to the tri-dimensional case for both principal and complementary series. We identify the one-particle subspace, generated by…
The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the…
For general nonlinear Klein-Gordon equations with dissipation we show that any finite energy radial solution either blows up in finite time or asymptotically approaches a stationary solution in $H^1\times L^2$. In particular, any global…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…