相关论文: On global attraction to solitary waves for the Kle…
Solitary waves of nonlinear Dirac, Maxwell-Dirac and Klein-Gordon-Dirac equations are considered. We prove that the energy-momentum relation for solitary waves coincides with the Einstein energy-momentum relation for point particles.
We present a comprehensive, nonperturbative analytical method to investigate the dynamics of time-dependent oscillating scalar field configurations. The method is applied to oscillons in a double well Klein-Gordon model in two and three…
In this paper, we consider the semilinear wave equation involving the nonlinear damping term $g(u_t) $ and nonlinearity $f(u)$. The well-posedness of the weak solution satisfying some additional regularity is achieved under the wider ranges…
We study the Klein-Gordon equation with general interaction term, which may be linear or nonlinear, and space-time dependent. The initial data is general, large and non-radial. We prove that global solutions are asymptotically given by a…
We investigate the inflationary attractors in models of inflation inspired from general conformal transformation of general scalar-tensor theories to the Einstein frame. The coefficient of the conformal transformation in our study depends…
This paper is concerned with the existence and regularity of global attractor $\mathcal A$ for a Kirchhoff wave equation with strong damping and memory in the weighted time-dependent spaces $\mathcal H$ and $\mathcal H^{1}$, respectively.…
We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null…
In this work we study the quantum and Klein-Gordon oscillators in non-commutative complex space. We show that the quantum oscillator in non-commutative complex space obeys an equation similar to the equation of motion of an electron with…
We prove that every solution of the focusing energy-critical wave equation with the compactness property is global. We also give similar results for supercritical wave and Schr\"odinger equations.
In the present paper, we work out the eigenfunctions of spinless particles bound in a one-dimensional linear finite range, attractive potential well, treating it as a time-like component of a four-vector. We show that the one-dimensional…
We analyse the Klein-Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting…
This paper is devoted to the quantitative study of the attractive velocity of generalized attractors for infinite-dimensional dynamical systems. We introduce the notion of~$\varphi$-attractor whose attractive speed is characterized by a…
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…
We are interested in establishing stability results for a system of semilinear wave and Klein-Gordon equations with mixed coupling nonlinearities, that is, we consider all of the possible quadratic nonlinear terms of the type of wave and…
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain cause the…
The long-time behavior of the solutions for a non-isothermal model in superfluidity is investigated. The model describes the transition between the normal and the superfluid phase in liquid 4He by means of a non-linear differential system,…
We prove that the critical surface quasi-geostrophic equation driven by a force $f$ possesses a compact global attractor in $L^2(\mathbb T^2)$ provided $f\in L^p(\mathbb T^2)$ for some $p>2$. First, the De Giorgi method is used to obtain…
The Gunn effect consists of time-periodic oscillations of the current flowing through an external purely resistive circuit mediated by solitary wave dynamics of the electric field on an attached appropriate semiconductor. By means of a new…
We develop the long-time analysis for gradient flow equations in metric spaces. In particular, we consider two notions of solutions for metric gradient flows, namely energy and generalized solutions. While the former concept coincides with…
The three-dimensional Klein-Gordon oscillator is shown to exhibit an algebraic structure known from supersymmetric quantum mechanics. The supersymmetry is found to be unbroken with a vanishing Witten index, and it is utilized to derive the…