Related papers: Klein-Gordon-Maxwell equations driven by mixed loc…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of…
Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of…
The variational method employing the amplitude and width as collective coordinates of the Klein-Gordon oscillon leads to a dynamical system with unstable periodic orbits that blow up when perturbed. We propose a multiscale variational…
A classical statistical field theory hidden variable model for the quantized Klein-Gordon model is constructed that preserves relativistic signal locality and is relativistically covariant, but is at the same time relativistically nonlocal,…
The classical Maxwell-Dirac and Maxwell-Klein-Gordon theories admit solutions of the field equations where the corresponding electric current vanishes in the causal complement of some bounded region of Minkowski space. This poses 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…
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 study solutions for the Klein-Gordon equation with vector and scalar potentials of the Coulomb types under the influence of non-inertial effects in the space-time of topological defects. We also investigate a quantum particle described…
The Klein-Gordon equation is solved approximately for the Hulth\'{e}n potential for any angular momentum quantum number $\ell$ with the position-dependent mass. Solutions are obtained reducing the Klein-Gordon equation into a…
We obtain some new Morawetz estimates for the Klein-Gordon flow of the form \begin{equation*} \big\||\nabla|^{\sigma} e^{it \sqrt{1-\Delta}}f \big\|_{L^2_{x,t}(|(x,t)|^{-\alpha})} \lesssim \|f\|_{H^s} \end{equation*} where $\sigma,s\geq0$…
The radial part of the Klein-Gordon equation for the generalized Woods-Saxon potential is solved by using the Nikiforov-Uvarov method in the case of spatially dependent mass within the new approximation scheme to the centrifugal potential…
The discrete static properties of a class of deformable double-well potential models are investigated. The Peierls-stress potential of the models is explicitely given. Numerical analysis of the equation of motion reveal different soliton…
We study existence and stability of standing waves for coupled nonlinear Hartree type equations \[ -i\frac{\partial}{\partial t}\psi_j=\Delta \psi_j+\sum_{k=1}^m \left(W\star |\psi_k|^p \right)|\psi_j|^{p-2}\psi_j, \] where…
We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove…
Horton, Dewdney, and Nesteruk [quant-ph/0103114] have proposed Bohm-type particle trajectories accompanying a Klein-Gordon wave function psi on Minkowski space. From two vector fields on space-time, W^+ and W^-, defined in terms of psi,…
We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small…
Solutions of the classical and nonlocal Gross-Pitaevskii (GP) equation with a parabolic potential and a gain term are derived by using a second order nonisospectral Ablowitz-Kaup-Newell-Segur system and reduction technique of double…
We consider the dynamics of even solutions of the one-dimensional nonlinear Klein-Gordon equation $\partial_t^2 \phi - \partial_x^2 \phi + \phi - |\phi|^{2\alpha} \phi =0$ for $\alpha>1$, in the vicinity of the unstable soliton $Q$. Our…
A de Broglie-Bohm like model of Klein-Gordon equation, that leads to the correct Schrodinger equation in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main…